I've used one in the past using a 1/2 ton pickup, so don't think you'd have any problems with the motor home.
Might be a good idea to crawl underneath and check your hitch attachment hardware: that's an area prone to corrosion.
If it were me and I found that the hitch frame was just bolted to the vehicle frame, I'd get somebody to weld it to the vehicle frame in addition to the bolts. Just me, tho.
I'm not familiar with the Class C motor home. As Big Iron noted, if it sags to where you don't like it or throws off your headlights, you can always add some air bags. I added an extra leaf spring on my 1/2-ton Dodge: kind of sucked when the bike wasn't back there: adjustable bags would be the way to go.
I did the same thing leogear did (I think). I had a guy fabricate two additional supports out of angle iron to stabilize the carrier to keep it from tipping from side to side on the central balance point: it worked out very well and made me feel a lot better about it being back there.