The battery might well be absolutely fine... If you have any problems with the new reg/rec then they should replace it, but there's no reason to assume it'll have been affected. I've been riding around with a broken reg/rec for a fortnight

Letting the battery run completely flat isn't a good idea as it can be
bad for it, but not always, this one's been flatlined a dozen times and still works a charm, as was my first one, it lasted 5 years. The one I had inbetween was a cheapy (don't know if that had anything to do with it or if it was just coincidence) and was knackered after I flattened it twice.