If you have a password set for unlocking the device from the lockscreen, that shouldn't affect your access to it via usb as far as I know.
Otherwise you could try adb, but that would require that you have usb debugging already set on your phone. If you don't, with a broken screen you won't be able to.
Food for thought for you and the readers. One of the very first things you should always do to a new android phone is enable usb debugging. it will not harm the performance of your phone, and it can be a life saver at times.
