It doesn't matter if the belt is 1 mile long. The rpms of the alternator are directly proportional to the size of crank pulley, the size of the alternator pulley, and the rpms of the engine. Put aside slipping for a moment, think of the belt as a bike chain, the crank pulley will rotate (x) amount and will move the chain x amount times the cranks size/ratio=

, the chain then moves y amount over the alt pulley rotating the pulley y amount divided by its size/ratio=alt rpms. It doesn't matter how many rotations the belt makes, what matters is that any movement of the belt transfers to adjoining pulleys. Sure a smaller belt can help with slipping but it will not make anything faster.