I don't think you will get reminded, there are a few apps that can do Push notifications for birthdays (but I don't use push). You should be able to find a few by searching, not sure if they are all free or what.
What I have done - and this was quite a mission, but am planning to automate it (dunno when I'll do that) incase other people wanted to use the same ...... I export the names and birthday info from my Windows Contacts, then create an ICS/iCal format file, I then dump that up on my Dropbox and then point Google Calendar to that (or you could just do a once off upload I suppose). I then have my Google calendars synced to my iPhone and pick to sync my Birthday calendar too. As the added bonus I have set up SMS alerts in Google Calendar so I get reminded via a SMS from them about a birthday/event.
