my understanding is without a battery [dead or alive] to complete the circuit the engine won't run - I'd do a proper static and load test of the battery before pulling the alt, although it may well be a bad alt
"When we tug a single thing in nature, we find it attached to the rest of the world" ~ John Muir "When we tug a single thing on an old truck, we find it falls off" ~ me Some TF series details & TF heater pics