Below is the Access Team's response. So no, you cannot use Access 2016 runtime with Office 365. You need to install Access 2013 runtime instead.
Note for Office Click-to-Run (C2R) users:
As stated in the past, Office C2R and MSI of the same major version cannot be installed side by side. Currently, if you are using Office/Access 2016 C2R, we recommend that you install Access 2013 Runtime MSI if you need a side-by-side setup. The two versions are functionally equivalent, and this installation should work smoothly.
—The Access team