Can you backup your files with an unlockable iPhone whose screen is broken?

I dropped my iPhone 4, underneath the screen, all the glass fell out around my button. Now, the touch screen is unable to be touched and my phone is locked. I can't get into my phone and my data is not backed up (poor thing I should start doing). Anyway, is it possible to plug my phone into iTunes and that can back my memory up? Or is there a way I could just fix the screen but the data is still there? Please, in need of important phone numbers and photos!

If it can connect to Itunes, then yes you can back it up, if not, your screwed