OK so lets assume that the OP does not want anything but a class A and wants to know if he can find a CLass A in his price range (after all this is exactly what the PO says).
Can you find a class A at $20k or under? = Yes
Can you find one that is mechanically sound for that price? = yes
Will it require some tinkering during the time you own it? = yes
Will it be a money pit? = unknown. There is just no certainty either way.
When looking for something look past the chrome and shine and look at the bones. Look for something with lower miles and with a proven chassis like a GM, Ford 460 V8 or even the Ford V10. These motors are basically the same thing as the motors in cars and trucks. That means that almost any garage can work on the basics.
Before buying check the oil for metal. Do the same with the transmission fluid. Make sure little things like the wipers, lights and that sort of stuff work. How does the exhaust look? That will be pricey to replace. How are the brakes? Basically all the stuff you would look at on a used car before buying it.
Now to the inside. Make sure the fridge works on both gas and electricity. This is an expensive fix if not working correctly. Depending on where you live you may need to check the AC unit (s). I live in the North East and have NEVER used my AC units. Check the heat out, make sure its in working order and so on. Just go through the unit and make sure things work as they should. All of this can be done in relatively short order.
Also be sure to drive it. If you cant drive it, you don't want it. No matter what bs the owner gives you, you just don't buy it without driving it.
Now as far as finding this for under $20k, yes it can be done all day long. I just sold a 1995 Damon 36' gasser for under $9k. It needed new tires, a new license plate holder and that is all it needed to be road worthy. The graphics were crusty and the toilet flush peddle needed to be reconnected but that's about it. It has 35k on the clock and ran like a top. If the new owner put a few grand into it he will have a great Class A for well under the $20k your looking at. furthermore there are NICER units out there than my old one. So keep your eyes open and you will find one.