AS I type this they are conducting a LP refill class here in the campground.. YES, if the campground lists LP then they should be able to refill your MH tank.
However: You pay "Campground prices" (kind of like a soda at a movie theater) as a general rule.
I like to shop around. I have on occasion saved as much as a dollar a gallon by visiting the right propane store (Usually a wholesale outlet). and sometimes it requires I go out of my way,, Like 50 yards out of my way :) (I'm not kidding)
Not this year but last (2012) on my semi-annula 800 Mile Hike back north (The other semi-annual hike is south) since I had to go to the west side of the state I came up the middle and turned left on I-94... on the way I stopped at the farm I grew up on, Now a propane tank farm. 2.69/gallon v/s 3/17 at the park I next visited. And since I know the roads in that area rather well, it was like 50 yards (all on the farm) out of my way from the road to the pump house to the turn around and 50 yards back to the road.
I had absolutely NO problem finding the farm :)