That can only happen if Gambit is solely in the OT timeline, which I don't think will be the case.
There have been unconfirmed rumors that Gambit will be in this Apocalypse movie. If so, his age will likely be around mid-20's (give or take). The fact that Tatum is cast effectively defines this.
If he is mid-20's in 1983 (which, by the way, would pretty much match what we were given for Gambit in the atrocity that was Origins) then there would almost be no way that we'd ever see Gambit and Rogue together.
In 1983 Rogue would be, around, -5 years old. That's right, she wouldn't even be born yet in this movie-verse. And it doesn't matter that Wolvie changed the timeline, conception is finite, and we saw her at the end of DoFP at the same age.
Now, if they keep Gambit out of Apocalypse, and conveniently forget that he (based on Origins) should be mid-20's in 1983, and instead make him mid-20'd in 2016, then this whole basteridized timeline of theirs becomes worse. In 2016, believe it or not, Rogue would be almost 30 years old. So I guess they could at least be compatible based on age alone, but that would very much kill any chance of using Gambit in main X-Men movies. Pretty much DoFP seemingly closed out the OT cast stories, and it doesn't look like we're going to see them back anytime soon. I guess they could use some of these characters, played by the original actors or actresses, in a Gambit movie, but the big question would have to be why.
Why put Rogue, who (IMO) was one of the worst characters (not the actress - love her) in the original movies, in with Gambit? I know, they were together in the comics, but the main issue was trust due to Gambit's background, and their inability to touch. Well, the whole touch thing has been done to death with Bobby, so no reason to rehash. And if there is going to be mistrust with Gambit then it makes sense it's with a cast that he can ultimately be a part of.
See, if they put him in Apocalypse then he can actually be a part of the team, and work with Storm, Jean, Scott, etc.
I just don't see them forcing Gambit into a timeline that is no longer the focus, mainly so he can have a difficult relationship with a poorly done character who has already had a difficult relationship...