Let me suggest that you already have enough information to answer this question. The roll you cited carries the date February 1864. This tell us that William Belote had not returned to his company since being wounded at Chickamauga. No word of his death or any other change in status had been received, so Belote was still thought to be alive at the end of February 1864.

The roll is sufficient evidence to rule out any suggestion that this man was involved in the fighting on Lookout Mountain.