For me, you can, but my definition of sweating a perm out is different. When I say "sweat a perm out", this means that I have just recently got a perm, and I participated in an activity that caused me to sweat a lot like working out, that caused my hair to "sweat out" the style.
However, based on your friend's definition, I don't agree with that. I think that sometimes when people have very thick hair and haven't quite figured out the best way to take care of it, they sometimes assume it is time for a new perm. When you first get a relaxer, you do the whole head, and in resulting touch-ups you do only the roots. I know that sometimes you do the whole head again, but that is at most a once a year thing. However, I do know people like your friend who get the whole head done all the time, but I would be personally leary of doing this.