Steven DeKnight has said in an interview (I believe an audio-only one on YouTube?) that it's possible for him to come back! I'll try and track it down, but he did say that it's possible. Whether they'll go through with it in the third, only God and Legendary know, but yeah. Also, on his twitter he regularly has conversations with fans, many of whom also root for this character, and when they ask if he'll be ok, Steven says as a part of a large creative team and an even larger movie corp (Legendary and whoever just bought Legendary) those decisions aren't always up to him. Charlie Day's also in favor, I believe, of developing Newt back from the ledge of villain and developing his relationships with certain other characters. So TL;DR, the actor and director are open to it, but it's all up to which plots/plot points get approved by the people above their pay grade.
Not to mention, this canon has one of the most interesting plot devices in sci-fi--the Drift is quite LITERALLY rooting around in someone else's brain--so IMO it would be dumb not to explore/expand upon the Drift itself, its other uses outside Jaegers and Kaiju, like psychological. If anything's gonna get the Precursors out of his head, I'd think it'd be Gottlieb fighting that battle in his mind that he's not currently strong enough to win.