There is 1 study vetting peppermint oil done on shaved mice. Mice do not experience androgenic alopecia and are, you know, mice and not humans. So their response might not be very relevant. In addition, we don't have very good anecdotal evidence for peppermint oil either. I've never seen anyone get significant regrowth with peppermint oil. I've seen it hundreds of times with minoxidil.
No reason you couldn't add it to your regimen though. It's pretty cheap and has no side effects. If it does help, even a little bit, then it's just icing. But I wouldn't neglect proven treatments like minoxidil in favor of it. Too little evidence to support it.