yes, it is you'll need stronger motors though
I'm thinking motors geared for high torque & low speed would be better suited than high speed motors. Like killerjackalope said, a relatively slow RC bulldozer or dump truck would probably have more suitable motors than one of those speedy Tyco vehicles that zoom over the terrain at 30mph.
Absolutely, though finding the right RC car for it would be tricky, something like an RC bulldozer or some such might be a good bet, also this project: https://www.instructables.com/id/Arduino-RC-Lawnmower/ Should be of some use, adapt to a hoover instead of a mower...
I was going to mention the Arduino mower in my initial question, but I ran out of characters - that's exactly the kind of mod I'm talking about. The RC vac doesn't need to be fast; in fact, slower is better, so it cleans better and you don't bash into things. An upright vac is a lot lighter than a mower, do you really think it would need larger motors than what a R/C car has?