Yes, but her despair when Madoka was still not a Magi stemmed from learning the harsh truths of what a Magi truly was, not just from her low self-esteem. She effectively gave into despair when she learned the purpose of the gem on her neck, but she only learned that because a certain someone was foolish enough to do a certain something with said gem. My point isn't that she wouldn't have fallen to despair, but that it actually should have happened later than it did, especially since it's depicted as happening around the same time.
Judging from what Madoka was telling Sayaka before taking her away, I'm assuming it had to do with that Violin Boy she was in love with and how Hitomi wanted him as well. There is no other explanation for it.