Yeah I think so. I think girls appreciate it because it shows that you're not afraid of admitting those things and makes you seem like more of an honest guy. I think it's rare for a girl to think less of you for doing it unless you were just being really pathetic about it haha.
Yes, it helps her to get to know you more as a person. The more someone open up to me then the closer i become to them. The bond becomes stronger. Knowing someone's insecurities and vulnerabilities is essential to get to know who they are as a person. We all have them.