Using the generator pulley will slow the alternator's speed down enough that it might not do a good job of keeping the battery charged at low RPM. Alternators are designed to run much faster than generators because there's no danger of throwing the windings out of the rotating assembly. Overspeeding a generator will cause the wires in the armature to break loose and drag on the field coil pole shoes. Alternators turn several times engine speed to assure a good charging current at idle.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!