What can happen to a dog if he is bitten by a groundhog?

Groundhogs can and do contract rabies and it is a concern. While they are not one of the most common vectors of the virus, a rabid groundhog isn't a pretty site and they will attack a person. They don't just carry it. If they get rabies, they will die from it.
If a pet is bitten by a rabid animal, staying away from it isn't going to help you AND it can possibly expose you to the virus. If it turns out you have a rabid pet, you and anyone who came in contact with that pet in the last 6 weeks or should be treated for potential exposure as well. Rabies is virtually 100% fatal (with 6 known survivors). This is NOT a disease to sit around and wait to see if anything happens.