The alternator does not double as the starter. They are separate units. The alternator is a belt-driven item that hangs off of a bracket at the 'front' (opposite end as the transmission) of the engine and is driven by the engine. The starter is a smaller electric motor that bolts into an opening at the transmission end of the engine and engages with a large ring gear to spin the engine for starting.
I don't think you'll gain anything using alternator power to wind up a spring for starting. You're just adding another step, a.k.a. a source of loss. If you only wind up the spring manually, or through regenerative braking, then you're onto something.
