What do you mean by homeopathy? Do you mean something diluted with water down to nothing? That's a big no. If you mean something else, I'd have to know what. Honestly though, replacement hormones are what are used to treat thyroid disorders. Things like diet and exercise and proper sleep might help, but it's not a treatment.
Hashimoto's has natural fluctuation. It'll change on its own even if you do nothing. Not proof of the "homeopathy" having any effect at all.
Another question, why would hair loss make a thyroid disorder less likely? You do know that Hashi's involves both hypo and hyper thyroid, right? Are you a doctor?