A bear will eat what it can catch. They are one of the major predators of whitetail fawns and turkey poults, but don't often prey upon healthy adults. I suspect if there are plenty of young groundhogs available, your bears will eat one if they can catch one. I wouldn't depend upon bears or coyotes to bring the groundhog numbers down to tolerable levels, though. Predators usually don't manage that as well as trapping or hunting.
I'm brain dead right now... this is tongue in cheek, right? I'm guessing this was a TV skit... if it was circa 1970... I missed it... first three years of college were spent sans television... not a standard back then... I think we learned more. Had a 13" B&W my senior year... my downfall.
BTW... papers were typed on a 3" Royal manual typewriter... spelling and punctuation counted... unlike the kee-rap they accept these days.
Sure hope the Jersey bears like tasty tender morsels of baby groundhogs but I'm not holding my breath.