They don't really need the Fox stuff for those types of mutations.
What Fox has the rights to is literally calling superpowered beings "mutants."
As to what can happen now, it is important to note that anything can happen if the head of Fox and the head of Marvel Studios makes an agreement to do it. That exact thing happened with Spiderman. Marvel still has no film rights to Spiderman: they were granted that privilege as part of an agreement with Sony. In the past, there have been barriers to making that kind of deal with Fox, but if it even looks like the deal will go through they could start making handshake deals with each other at any time if they wanted to start cooperating sooner than later.
It is less about who has what rights, and more about who's willing to make what deal. For example, if the head of Fox studios calculates the deal will go through, he may start taking Alan Horn and Kevin Feige's phone calls, since he's likely to be working with the later and for the former soon.