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.
trkyhntr
No man's life, liberty, or property are safe while the legislature is in session.
--Mark Twain (1866)