I hadn't seen your thread, but I have thought about this at some length as I ruminated about what spirits actually are. The short version is that I'm not sure.
At first blush... I'm inclined to think that no, he isn't a spirit in the conventional sense of the word. If you're talking about "spirit of wisdom" in the sense of "incorporeal Fade entity that represents a single aspect of the psyche," AKA "the Maker's First Children," then no, he's more complex than that. He himself says that these spirits have distinct identities and their actions and thoughts are defined by their natures. He has a very strong sense of purpose, it's true, and I do understand the connection between wisdom and pride/solas, but he can learn. He is capable of growth. He does not believe that spirits are capable of these things. So, by his own definition of the word, I don't think he's a spirit.
But Solas - like every other living creature - has a spirit. Every sentient creature has a spirit that crosses the Fade upon death. Humans, elves, and qunari are possessed of spirits who enter the Fade in dreams, as well. Their spirits inhabit their bodies and are intimately bonded with that body and no other, but that doesn't mean that the spirit is bound to their body always (except for dwarves and Tranquil, that is). So, bonded but not bound, to take a page from Cole's ledger. These spirits are multi-faceted, capable of the full range of emotion and motivation, and they are capable of acquiring new aspects as they learn or as they "experience more of life to learn more of the Fade." Solas seems to be especially proficient at sending his spirit into the Fade at will. The bond between his body and his spirit is not as strong as that of people born after the creation of the Veil. And his spirit, while more flexible than pure spirits (according to his definition), may be more rigid than that of people born after the creation of the Veil. His spiritual identity is strong and he can cross the Veil with ease, but he's a little less adaptable than the quicklings who inhabit the modern world.
An Inquisitor with the Arcane Knowledge perk describes the Veil as a magical vibration that repels the Fade. It serves as a barrier to spirits in both directions. Solas can slip through because he knows how to get in phase with it (just as some spirits and demons discover by accident), but for most, it's an effective barrier.
I guess what I'm saying is that I see the spirit/mortal existence as a continuum rather than a pair of binary absolutes. I see true spirits, entities without a corporeal body, at one end of the spectrum, and I see dwarves, mortals whose spirits are completely and inseparably bound to their bodies, at the other. Ancient elves may have fallen somewhere around the middle, with modern elves, humans, and qunari falling closer to the "bound" end. I freely acknowledge the probability that individuals may fall outside the expected range for their race. All are "people," sentient entities, but their ability to interact with magic varies.
Dagna says that dwarves can't move with the flow because they're part of it. I think that's a reference to lyrium, the source of all magic. Their bond with the Stone (and their spirit's bond with their bodies) is so strong because the lyrium is part of them, their physical or psychic existence. They can't flow with magic/allow their spirits to leave their bodies because of their bond with lyrium/bond with their bodies. I don't know if that makes sense.
When people are made Tranquil, they are often described as having their link with the Fade severed, but I would say rather that the bond between their spirits and their bodies is cemented with the lyrium branded onto their skin. If a spirit touches their mind, it breaks the glue and they're restored to what they were... assuming that pieces weren't torn when the bond was severed.
So, I guess I both agree and disagree? I do believe that Solas is a little closer to being a spirit than most people we've met, but he is still bound by his corporeal form.
TL;DR: It's complicated.