Could replacing the alternator on my '07 Camry improve my gas mileage?

I know that the alternator keeps the battery charged, and has nothing to do with mileage.

However, consider that the battery was unhooked for quite a while and all the pre-sets on the car (radio, etc) were lost. Is it possible that there was a hitch in the computer that was re-set when the power was removed for a while?

I swear the car was getting to be like pouring gas on the ground before the alternator replacement, and I went nearly 500 mile on the next tank of gas.

I could be hallucinating, as I had not clocked the “before” mileage.