Champion Generator & SurgeGuard - Ground-Neutral Bond req'd?

Yes, you can use a ground to neutral bonding plug on the Champion generator. I don't think this is your problem, however, from your description. If it were a ground to neutral bond issue, I don't think you would ever get power through your surge protector. I think you are getting a voltage drop, or surge when the A/C starts. Just too much for the Champion to handle all at once. You might have to disable other loads when you want to run the A/C.