The way laser hair removal works is that it kills the follicle altogether. So no, unfortunately T won't grow it back where it was removed.

I was in the exact same situation a few years ago though, and I did a ton of research and presented my mother with all the possible dangers, ranging from permanent discoloration of the skin and burns, all the way to death (indirectly, from people applying too much numbing cream prior to the hair removal and overdosing).
Granted, I played it up a bit to make it sound more dramatic than it is, since it is relatively safe procedure, but my goal was to stress that getting rid of my 5 o'clock shadow wasn't worth the risks. I don't know if that would work with your mom, but it's just a suggestion. You could also suggest a compromise of sorts where you make sure to shave, or wax, or do some other form of hair removal that isn't permanent. Good luck.