In theory this could work, but it would probably not work very well with a regular combustion engine without some modifications. You could potentially use highly compressed air to drive the piston (in the IC engine) instead of a the combustion of gasoline. Essentially, the other steps would stay the same. See the following link for an explanation of the IC engine...

On another note, some folks are using compressed air to power vehicles with engines that are optimized for using air rather than a combustion fuel. Remember though, that compressed air is not an energy source, but just a medium. Work has to be done to compress the air. If you use a compressor that is powered by electricity, you will be essentially using coal (or whatever is supplying you with electricity) to compress your air, and in turn run your car.