365 is really all about being an annual subscription. You can have for example, version 2016 with 365 or a stand alone purchase. 2016 will open an mdb no problem, and IIRC it won't prompt you to alter it. For your own peace of mind, you could save a back end (be) copy for insurance (which you should be doing on a regular basis anyway) and convert your production version to accdb. Unless you require some special feature that applies only to your be file, I doubt you'd have any issue just leaving it as is.
BTW, M$ seems to have altered their stance on 64 bit vs 32 bit and now seem to default to 64. Unless you need some very specialized data types, I'd go with 32 bit Office. I'd check that out for you situation. Here's one point of view
https://www.devhut.net/2017/04/13/ac...compatibility/
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.