I kind of doubt it, honestly.
In the new Thrawn book, he talks about helping the Empire fight unknown threats from the unknown regions. I'd think that if he ever did join the First Order, he would leave after Snoke took over.
Or maybe he'd just go Heir of the Empire and die before the Sequel Trilogy even happens anyway.
Dave Filoni confirmed in November that Lars Mikkelsen's Thrawn outlives Mads' Galen Erso in Rogue One. In other words, Thrawn and Ezra lived past Rogue one, and possibly even original trilogy. How, thats completely another story.