I believe mushrooms do grow back if you just pick them, but if you dig them up, then they are permanently gone.
I find that just dropping monster meat and grabbing manure from beefalos to be less time consuming than feeding pigs. Fuck the pigs. They are more or less useless unless you get a whole posse. Two pigs get raped by a tier 2 spider nest. The only thing pigs are good in my opinion are providing skins for pigskin helmets and for drawing hostile mobs to.
Their king is kinda cool though...gold for useless trinkets.