You're right to be concerned about the weight and balance issues. Whether or not it's practical will depend on the individual motorhome you're looking at. I think the majority of class C hitches are not rated to have more than 500 pounds tongue weight (and a good many have a lower tongue weight rating than that). You'll probably be pushing 750 pounds by the time you get a carrier and associated odds and ends to get the motorcycle up and down.
There are a few things specifically to look at. The first, as mentioned above, is the tongue weight limit of the hitch. Do keep in mind that the farther out from the back of the motorhome the motorcycle is, the greater the lever action on the hitch will be, so it would be wise to look for some cushion here. It would be wise, in my opinion, to have a qualified shop check out your ideas and probably fabricate a mount that mounts to the frame directly rather than just the receiver hitch.
The second is the gross vehicle weight rating and associated carrying capacity (basically the gross weight rating minus the weight of the motorhome with nothing in it). As a general rule, for full-timing in a class C, you'll want to look for the largest carrying capacity you can find; 1500 or 2000 pound is not atypical, and by the time you get water, your motorcycle, and yourself, you'll have used up a significant portion of that.
The third thing to check is the axle weight limits and the actual axle weights. Adding a lot of weight to the back of the motorhome will cause the front axle to be unloaded some and the rear axle to be loaded more due to the vehicle as a whole acting as a lever. You could be adding maybe 1000 pounds to the rear axle and removing 300 or so from the front axle, as a very very rough example/estimate. Of course this also depends on the wheelbase and overhang of the particular motorhome.
There are a few other alternatives to porting a motorcycle around that might work better. You may be able to create some sort of a front mount, which often works out somewhat better from a weight distribution point of view (but has its own challenges with engine ventilation and headlights and protecting the motorcycle and so forth). There are also some single-wheel dolly mounts available for the hitch where the front wheel of the motorcycle gets strapped in while the rear wheel rolls along on the road. Finally, you could always get a little trailer of some sort to carry the motorcycle, and whatever else you wished to carry.
I know you didn't ask about it, but please make sure you have reasonable plans for where you'll generally be staying/parking and how you'll handle water, sewage, electricity, and so forth. A long-term site at a campground is, of course, a viable way to do this and shouldn't cause much if any hassle. On the other hand, simply parking on the street or similar situations is not taken kindly to at all by many California cities.