He might, but there might be way to convince him it's still worth living for the sake of his love or his friends. If we've managed to convince him Thedosians are real people, he might see some value in helping them, even if saving his folk has failed. He clearly showed some care and desire to help when we took him around in main game.
Also even if he's left with nothing, his guilt will still be there, it might even intensify. And I think that's what's keeping him alive, he always wants to be able to fix at least something.
However we do it, it will be a very very painful process for him, redemption for deeds like his doesn't happen easy. He'll need friends and/or his beloved to get him through it.
I don't think anything short of redirecting his purpose along a course of action that he genuinely sees as worthy of his full dedication, will do it. Solas seems to be the sort who needs a purpose, and it can't be something as simple as the pursuit of knowledge, either. As much as he might seem to prefer the company of books and spirits, he's not the sort who seems able to ignore the suffering of beings. And yet he also seems to be the sort to trust his head first and regret greatly with his heart, later - making him different from, say Cassandra, who is similarly devoted to her mission, but seems more willing to make the leap of ''what feels right" and be able to change course when she's at a loss. Solas seems way, way, more stubborn than even Cassandra. Both his head and his heart will need convincing, and I'm guessing he will need lots and lots of direct, full-sensory evidence that his way is wrong, backed up by a completely convincing and irrefutable argument that both the world AND his own conscience would be better served by not destroying the world. Which is the thing that worries me. It may take a lot of destruction before he's convinced. And that puts me in fear of the 'kill yourself to right your mistakes" ending, or similar.
Or ... who knows, maybe we just need to recruit Thedas' best debater. With Solas, the final boss fight could be a three-hour conversation tree 