Most wires intended to be installed under a bolt or nut will terminate with a ring terminal - what color is the wire?
I've never seen any vehicle, Sidekick or otherwise, leave the factory with a ground wire attached to the alternator case, and bearing in mind that the two generation of Vitaras/Grand Vitaras didn't come with it, I'm wondering where you saw that schematic. The norm is to have the alternator bolted directly to the engine and the engine grounded to the battery negative with a heavy lead that is intended to be the return for the starter, a separate ground for the alternator is usually not necessary, installing one will not cause a problem, but I would not expect it to change things significantly.