I have always ran my batteries to the mods cut off, from my very first mod up to now.
As has been said, mods cut off before a battery reaches a point of damage. My lowest cutoff is on a DNA75, which is 2.75V soft cutoff in Escribe, then the Alien which I believe is 2.8V a cell, so 5.6V in series.
Most are a fair bit higher than this with at least 3V+ per cell. I still have batteries from over 2 years ago that work well.
Your batteries are fine to use
.