We do not know except he has not been seen in Early Access Act 1. Elves can live a long time though. There has been nothing confirmed regarding this. However Drizzt is in Forgotten Realms and BG3 is Forgotten Realms while Solasta is Badlands so it would be impossible to meet Drizzt in Solasta.
I gotta ask, what's with this Solasta obsession of yours? This is the third or fourth post I've seen recently where you bring up Solasta in an entirely unrelated conversation. The OP didn't mention Solasta. The OP doesn't have a history of mentioning Solasta, so it's not like you're making fun of them. Solasta doesn't even have drow. And if you just wanted to tell the OP any games that might possibly have Drizzt, then Dark Alliance would be the go-to mention.
The rest of your post is decently informative and helpful, but this line is just wut?!??? You don't even seem to like the game much, so it's weird why you keep bringing it up...
Relevant to OP's postI'll add that Larian doesn't really do expansions, so it's unlikely that we'll get any story-DLC at all, let alone with Drizzt. But BG3 does have Volo and Minsc, so Larian has already shown their willingness to have famous D&D character cameos. In BG3, where drow are a big enough presence to be a playable race, I'd guess that it's likely we'll see him.