I don't think "destruction of all non-ancient elves" is Solas's goal, but it's likely that many people will die as a consequence of his actions.
Let's look at the evidence we have seen and draw a conclusion from that:
- When Solas brought up the Veil, we see that humans rose to power, and elves became mortal.
- Because elven cities were created at least partly from the stuff of the Fade, they mostly crumbled to ruin.
- The world of the eluvian network began to fall to pieces because it relied upon the Fade.
- Elves who were in the eluvian network at the time were trapped or perished.
- Elves who were in uthenera were unable to awaken whereas this had been possible before (and we seemingly encounter such sleepers in The Descent... they are in coffins), with some exceptions (Abelas and the Sentinels were called to wake to defend the Temple of Mythal--it's likely there are other similar groups of elves in remote areas).
- The elves "lost everything, even themselves." We don't know what this means for certain, but it's probably a big factor in whatever it is Solas thinks is wrong with the world and why he thinks it's necessary to fix it.
- Hundreds, maybe thousands, of species went extinct due to the absence of the Fade. There's a codex entry about an elf dying with the last of a gigantic, magical flower species. It could be one reason why griffins went extinct--we are told the ultimate reason for it in Last Flight, but they were already rare enough, and had enough difficulty breeding, that only the Wardens had access at that point. Pre-Veil they may have been fairly common, or at least didn't have the same difficulty reproducing. The creatures that went extinct didn't die because they were never part of the real world, but because, whether or not they were created by the elves, they relied on the Fade to exist.
- We know that the world in the eluvian network "remembers" how it used to be, so you can restore certain parts of it.
- It's probable that certain cities were destroyed so entirely, due to their reliance on the Fade, that there is no trace of them at all. Arlathan might be one of these.
- In the "real world" in game in DAI, we see gigantic melted looking rocks. These might be the remains of floating cities/crystalline cities and towers of ancient elven origin. It makes some degree of sense that this would be so, because there are also surviving underground temples/tombs. The more rooted in the mundane world, the easier it is for it to survive...
- The Titans are sleeping and seem unable to wake. It's unclear whether this is good, bad, or neutral...
- Dragons no longer rule the skies. We don't know for sure what this means, but I suspect pre-Veil dragons were a bit... more. They're beasts in modern Thedas, but maybe they were something else pre-Veil.
All of this destruction happened because Solas changed the nature of the world, or at least the perception everyone and everything had of the world. But something important to note is that not everything died. Even the elves, who were heavily reliant on the Fade, did not die. They quickened, but they adapted. They created their own cultures. But because the elves were greatly weakened, humans were able to take over and overthrow the elves who once ruled over them. (This may, if you want to get into overanalysis mode, have something to do with why humans attributed the creation of the Veil to their Maker. If their god did this, then they can then claim that they are the Maker's chosen race. More reason for keeping the other, "less deserving" races out of their religion. It's ugly, but this kind of thing happens in real life too.) Yes, the destruction was massive, and it caused a mass extinction. Pretty much everyone's civilization was likely destroyed, even the humans'--assuming they had one. The dwarves' society likely changed, too, without their Titans.
So my answer to the question is: Yes, it'll kill modern elves. No, it won't kill all of them.
What we can expect, if Solas succeeds, is that the Fade will "remember" how some things were, while it doesn't others. Ancient elves who were unable to wake from their slumber will rise. There may be more of them than there are modern elves; we don't know. Those melted towers may rise back into the sky. Buried cities will break free from the ground. So: Earthquakes, people being trapped, people falling. Cities sinking, rising. Statues that were crumbled reassembling themselves. Everyone is suddenly connected to the Fade; if it's like the eluvian network, everyone but the elves will be sickened by it, and possibly weakened. But that may only be a feature of the eluvian network, meant to keep anyone but elves from entering. Remember that humans did exist pre-Veil, and there are a few hints that qunari also existed pre-Veil, in some form or other. Some of those horned statues predate the Tevinter Imperium, so the conclusion to be drawn is that either the elves created the qunari, or the qunari already existed and were possibly enslaved by elves.
The qunari are terrified of what may happen with their Saarebas if Solas succeeds. Apparently they think the Saarebas will become even more powerful, or... something. I'm not sure. But they clearly believe it's going to be really bad. However, take that with a grain of salt, because we know the qunari are terrified of magic and spirits in general, hence why they treat the Saarebas as they do. It's not necessary to treat their mages that way, but they believe it is. Remember, we can play as a qunari mage. Although Saarebas might be particularly powerful for whatever reason, they certainly could be the same as any other mage.
What we cannot expect, and what I'm sure Solas does not expect, is that everything will be exactly as it was. Species that went extinct will stay extinct, unless like the griffins something was done to preserve some fragment of them. Cities that were heavily damaged might "snap" back into place, but they will remain damaged. If the Black City were ever golden, then it nevertheless will not be restored to its former glory (I suspect it's blighted...). I also don't think the modern elves are going to immediately regain immortality. Their children might, or their grandchildren, but that's presuming that they survive to have children (meaning if the chaos that ensues or the ancient elves don't kill them).
A lot of people seem to think Solas is trying to do this out of guilt, or nostalgia. Nostalgia has nothing to do with it. Guilt probably does, but if it's guilt then I think it's guilt over a broken world. Remember when I pointed out that quote above about elves "losing themselves?" We don't know what that means, but it's the key to why Solas feels he MUST go through with his plan, even if he has come to see the modern people as, well, people. I don't even think he really wants to restore the world exactly as it was, he just wants to fix what he broke. And then he wants to make things better (i.e. no evanuris, no slavery...).
People say Solas intends genocide, but that's not actually what Solas is up to, at least from what I understand. He doesn't want to kill everyone. He thinks that it's inevitable that most if not all will die--if not from the fallout from his plan, then because the ancient elves are likely to go on a killing spree. But this does not mean he's setting out to specifically kill them, which I think a lot of people misunderstand. Note that Abelas spoke to you as if you were a lesser being... well, most if not all of the ancient elves are likely to see non-elves and modern elves the same way. Although Solas doesn't want a world with slavery and does want people to see each other as, well, people, he ultimately won't be able to be judge, jury, and executioner for everyone who disagrees with him. He's super powerful, yes, even for an ancient elf. But he's not powerful enough to protect everyone ever.
Of course, all that said, even if there are some (or many) survivors among modern elves or, well, everyone else? Even though I don't think Solas is out to commit genocide, going through with his plan while knowing the fallout of it will be terrible is atrocious. But he hasn't done it yet, and there may be ways to achieve his goal (fixing what's broken, making everyone whole again) that would be less catastrophic.
As for why modern elves seem to want to follow him... we can't be sure that all of them are modern elves. But, among the oppressed (because let's face it, even the Dalish are oppressed in Thedas--always hunted, always having to move because the humans don't want them around, struggling just to get enough food and supplies to survive while they slowly die out, picked off person by person and clan by clan), even knowing they might die, they might be willing to do so because they will accomplish something they feel is worthwhile with their deaths. And they may also not die. Solas doesn't like to lie--he'll happily omit truths, but he rarely tells a direct lie. It's actually easier for him that way, because he doesn't have to remember all of the lies he's told if he only omitted truths (i.e. he grew up in that village thousands of years ago...). So he might have conveniently failed to tell the elves that his plan might lead to their destruction. Or, he told them and they are flocking to him anyway because even though there's a high chance of their demise, there's still some chance they will survive to see a better world.
And edited to add:
I also believe Solas's plan will lead to the deaths of many ancient elves. Again, his goal is not genocide; thinking so is a misunderstanding of what he's trying to do. Killing everyone other than ancient elves is not his goal, but it's something he sees as an inevitable side effect. He wants to restore the world, and fix whatever it is that he sees as broken. This may be good for the dwarves because it will probably mean the Titans will wake. It will be bad for nearly everyone else (ancient elves included, because of the Titans...), at least in the short term. But Solas seems to think that modern people are somehow not "whole." Hence why he compared them to Tranquil. And like the Tranquil, "fixing" them might destroy them (remember the healed Tranquil who was simply unable to control his emotions... giving access to magic/spirits to people who never had it, would have similar results). In my opinion, the mages are the most likely to be okay if Solas succeeds, because a large part of what is "wrong" appears to be the lack of magic, and perhaps a lack of connection to some spirit-self that elves once had, but no one has anymore. But that does not mean that all mages will be fine, or that mages won't suffer any problems at all. They are just the ones who have the best chance, because they are already on some level familiar with the Fade.