Yes, you can have AI and full version installed on the same computer without issues. Full license on a dongle and AI license as a software version works great.
If you have a spare AI 7 license I would be very happy if you could donate it for my studio Mac.
I too have sometimes trouble remembering to take the dongle with me, so an AI installation as a backup would be very useful.
Shout out also to anyone else who has so many AI 7 licenses they don’t know what to do with them. Now you know.