I think this is very true. He's also spent most of his time, possibly thousands of years, asleep. Everything must feel sort of...off. Not real. Nothing he knows is what it is supposed to be. If you look at the Exalted Plains, you really get the sense of the world as we know it being somewhat post-apocalyptic for anyone who remembered the greatness of the old days. Just endless ruins and graves.
I don't think he views the time itself as being unreal, since he can't travel through time. But I think he may have originally given the orb over to Corypheus with the thought that so many people had already died, what difference did a few more make? Especially if what he intended to do would fix things.
I do suspect that "realness" to Solas is a matter of being... uh, for lack of a better word, literally "dimensional" within the game.
If banter with Cole is to be taken literally, Solas' connection to the fade represents a significant distinction between him and most mortals of Thedas. He exists fully in both places- he inhabits a dimension they do not.
It's... like 2D vs 3D. Not to get too meta, but in a way Solas' initial attraction to Lavellan is a lot like ours to him. He's fantastic, he's incredible, but at the end of the day, he's not really real, like we are. She is his Waifu, and he's willing to lose himself in the fantasy because hey, why not? It doesn't hurt anyone. His instincts are still compassionate, (just like we might choose to save a Druffalo, even knowing it's just a few paragraphs of code), but his obligations to these "shadows" and the depth of his connection to them is necessarily limited.
It doesn't map entirely of course, but let's say someone had a hostage at gunpoint and threatened violence unless we logged in and let Solas die repeatedly to a Hinterlands bear. Would anyone hesitate? We might feel a teeny twinge of guilt while we did it, but there's no real question that we would. Because real.
Of course, in-game, at least, this dimensionality is (potentially) restorable, which complicates things. It's more like... having to make the choice to sacrifice him with the knowledge that if you didn't he might, eventually become real. Much harder decision. He's not, but he could be.
And of course, in Lavellan's case, she already is. As Cole points out, she's even brighter than Solas is, present in both dimensions in game, as well as outside it (3D us whoo) and eventually Solas realizes this as well. His myopic focus on the orb, goals, and duty prevents him from seeing this in a non-Lavellan Inquisitor, but she forces him to look.