From 1307 datasheet:
Quote:
VBAT – Battery input for any standard 3V lithium cell or other energy source. Battery voltage must be held between 2.0V and 3.5V for proper operation.
Yes, for backup, it should work fine with a flat battery becuase when it is powered by the MCU, it does not use the battery. That is why you can ground that pin if you don't need backup.
Mowcius