If you ride a quad at home on dirt and rough gravel tracks you will probably be fine around arillas, if you don't ride at home it wouldn't be a major surprise if you had an accident on what are compared to british roads, poor surfaces. Quads are surprisingly easy to turn over if you don't know what you are doing and the injuries you get are often worse than you would have with a two wheeler.
We have had bikes in corfu in the past, but I've been riding at home for 25 years, Corfu has different hazards such as olives on the road, poor surfaces and coaches or 4x4's on narrow lanes so I'm still extra careful, and I wouldn't have taken my kids on a bike in corfu, though I did at home.