The only issue with running the AC while driving down the road is vibration.. And AC's often vibrate no matter if you are moving or not.... And it's going to vibrate when you move down the road running or not, so don't worry about it
Many folks use the Generator to run their AC, be it rooftop or basement and most have no problem. In fact, I can think of a reason for doing so.
Generators like to streatch their legs from time to time,,, They sit too long they get cranky, Running the AC when you are driving exercises the gen-set and that may well be a good thing