On button press, use battery if no power is provided via USB
It seems this doesn't work. I measured the circuit with 5V applied, but no battery. At the battery socket measured 5V and 5mA when I shorted it to ground. So the transistor seems to act like a 1K resistor.

Second problem was that the IC has clamping diodes. So when the circuit was off a current would go from the battery, through the pull-up and the clamping diode, to VCC. Lowering the value at the Base, resulting in even more current leaving the battery. A few milli-amps total. Enough to have the battery run low pretty fast.

Nice idea, but it didn't work out )-: