Yes, hair has no relation to your spiritual power in any shape or form.
I feel like it might have a slight effect. Whenever I had to cut my long hair, I always felt like an NPC afterward.
Just watching videos of people with long hair getting their hair cut short and seeing their facial expressions is enough to tell that it takes a slight toll.
Historically, long hair has also always been regarded as a sign of vitality. Also, I don't think most of our Gods being depicted with long hair is just a coincidence.
Another possible reason this might affect one's spirituality is beauty. I think long hair is attractive on both men and women. Of course, this is a subjective opinion, so don't take my word for it. Search "celebrities with long hair vs. short hair" and decide for yourself.
I think both genders look better with long hair. When you feel more attractive, maybe you get compliments on your hair, it obviously affects you positively.
Of course, you don't need long hair to advance spiritually. If this was the case, people who are more inclined to lose their hair naturally, or even go completely bald, would be doomed. But that's obviously not the case, and everyone can advance on this path.