I don't know what being a female has to do with your post. Good tips for a founder of any gender though.
By all means apply! But have a backup plan. I have known people that have looked for funding only from YC. That's just as silly as only applying to Berkeley and then giving up on your PHD if you don't get in. As they say in football, that's not a high percentage play.
There were plenty of women PHDs at my graduate school, and men too! So I know people of many genders can navigate processes with lots of rejection.
They psychology of these things is quite complicated.