Mark,
Not directly (to my knowledge).
3ds Max does allow you to save to a previous version; so as long as you remember to Save-As from the 2017 before going to the College's 2015 computer you should be okay.
Check out this:
https://knowledge.autodesk.com/support/3ds-max/learn-explore/caas/CloudHelp/cloudhelp/2016/ENU/3DSMa...
Also, I would recommend you keep your files small; make individual parts parts or areas as files, then merge them all into a final scene. That way if a file goes bad, loses a new feature/translation, etc. you haven't lost everything and can continue to work with the bad area missing/etc. Otherwise you'll be dead in the water until you can return to your other station.
Also, you can sometimes still download older versions of the software. I know the subscription option allows this; I'm not sure if the student version (which I assume you are using) has this option, but it is worth looking into.
Hope that helps,
-Kenny