I'm not sure many people would have a desire to eat a groundhog after getting whacked by a powerful varmint rifle. They can sure get unzipped pretty good. I've also shot ones that were mangy, covered in ticks, you name it. Not judging people who have, or do eat them though. Maybe their methods/spots differ greatly than my own.
I will say this though~our harsh 2013/2014 winter didn't seem to do much damage to their numbers. It's been a busy spring. :) Cool weather and regular rain has they hay impossibly high right now...so it'll be quiet in the hay/soybean/grain fields for a couple of weeks. One wandered into a young corn field Saturday while I was out for a hike with the .204 R though.
***EDIT~just got caught-up on the groundhogs, forgot the question. To the best of my knowledge, for groundhogs at least, they're considered pests and not fur-bearing, or game animals at all. No season, no limit.