As long as the bitness is the same, you should have no issues. If not, then maybe, and most of those issues relate to the use of API's used in 32 bit versions. They usually have to be modified for 64 bit - not a huge thing. If you have any choice or say in the matter, get them to install 32 bit version of Office. It used to be the default but M$ has made 64 bit the default without providing any escape from the issues. IMO there is no present need for 64 bit Office. In Access, it allows for a very large number type which most people don't need. AFAIC, 365 is just the new name for Office and what used to distinguish between the subscription version of Office vs the installed version. I use Office 365 with Access 2016 - but 32 bit for sure.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.