Hope this is the case, but my experience goes against it. The alternator should make enough electricity to run all your lights and accessories, without any assistance from the battery. About the only battery fault that could prevent this is a shorted cell, which should have alerted you by nose if by no other sense, as the remaining 5 cells spewed gas from overcharging.

However, replacing a battery with a fully charged one, will offer the assistance needed to an alternator with a slipping drive. Time will tell, and not enough of that has passed yet.
--
Art Benstein near Baltimore

If you keep your feet firmly on the ground, you’ll have trouble putting on your pants.