Interestingly, it seems that this use might be acceptable.
From Collins via The Free Dictionaries
n, pl -phies
- (Pathology) a wasting away of an organ or part, or a failure to grow to normal size as the result of disease, faulty nutrition, etc
- any degeneration or diminution, esp through lack of use
vb, -phies, -phying or -phied
to waste away or cause to waste away
So, the implication is that there is degeneration or wasting away. And this could apply to each individual hair. They're frizzy because they've wasted away, individual scales have fallen off and the hair is dry.
That said, I would consider it an unusual choice of words in this context given definition 1 above. It's more usual to apply this to an organ or some fleshy part. You can tell that from the synonyms given in thesaurus.com:
And also from the ngrams. If you follow the links to the few cases where "atrophied hair" is actually used, it is normally along with "follicles".
My own preference, would be to use malnourished. If you check with a quick google search, "malnourished hair" gets about 6x the hits that "atrophied hair" does. The conditioner would provide nourishment for the hair. It's probably a safer choice.