Yes, it could happen, but it probably won't. The Uniate churches are Catholic churches that schism ed in the past but were reconciled with the See of Rome. So it definitely does happen.
It's happened before on a grander scale. A number of Orthodox Churches reconciled with Rome a very long time ago. They are known as Eastern Rite Catholics today. A goodly portion of the Anglican Church will soon reunite with Rome, and I'm guessing a goodly portion of Episcopalians as well.
God willing, the entire Church will become one again.
I heard that some of them are asking to merge.The pope is considering it. The ministers who have wives are allowed to keep them but the ones who become ministers in the future are not allowed to marry.
Thirty years ago there was some idea that might happen, and there were even an extended series of discussions on the subject, but in the end the Catholics thought that they were just going to mount a take over of the Anglican Church, so it floundered.
I don't think anybody today has any real expectation of there being a merger.