I have an Access 2013 runtime installed on a Windows 10 PC that has also Office 365 installed. When I run an Access 2013 database (backend is in MS SQL server 2014) it works well for three weeks now. But now there are two opinions on this:
One is that it is working well and there are no issues here in terms of compatibility.
Other one is: No, it can’t be installed side by side on one PC. It will cause conflict between the operation system; MS Outlook and OneDrive sync process and it will also be a problem for Office 365 licensing and warranty.
If you have a version of Office 365 without Access installed there will be not a problem.
Access Runtime is free for using your database without a full version of Access.
If you will upgrade or additional install a full version of Access you need to remove the runtime version first probably. More problems can be expected when you install different 32bit and 64bit versions but that is another story :):).