At one point in my life I had grand plans build a flywheel into a four wheeled bicycle. I could replicate regenerative breaking, I could spin up the flywheel at stop lights, it was going to be great. I mentioned this idea to a civil engineer friend of mine, who pointed out that I could probably get better power density with a battery. When I realized I'd reinvented a heavier version of the electric bike I wasn't so excited about the project.
Not if you keep it level enough, which should be feasible on a four-wheeler. I mean, the gyrobus shows that it's not a infeasible concept - they still let people ride it sometimes here in Antwerp, as a curiosity: http://en.wikipedia.org/wiki/Gyrobus