Yeah, he's going to stuck on the Texans this year. Best case for him is all his court cases to be handled civilly, and get an excellent PR team to go on a redemption tour in the offseason, and then force Houston to trade him for a fresh start.
These things aren't unheard of. Mike Vick came back and has been widely accepted, though he's done a ton to rebuild his image and his crimes weren't so severe. Countless players have beaten women and gotten DUIs, etc, and Ray Rice has pretty much taken the heat for all of them. Ray Lewis probably killed a guy and lied about it, and hardly anyone talks about it. Hell, Jameis Winston has several cases similar to Watson's but because Jameis is a funny meme player (lol he throws a lot of interceptions and he got LASIK) nobody really cares either.
A player of Watson's caliber will have a great team to fix up his image assuming he's not criminally convicted. He'll always be remember for it especially in this era but good enough play can wash away anything.