For an aircraft starting at the gate with bleed air, the aircraft's APU is most likely INOP awaiting maintenance.

I had to do some ground run ups and the ground crew would connect a hose about a foot in diameter that would supply the bleed air. We did this right before pushback, and usually the #1 engine would be started using the bleed air. It was loud. The ground start air supply was a large diesel engine that would turn a large compressor which turned really fast to blow high velocity air.

During this time the GPU would already be connected (from when the aircraft was secured at the gate) directly below the cockpit and that would allow the avionics to work on the aircraft. It is 115 Volts AC and most aircraft that run a primary DC bus would have an inverter (rectifier). The battery would never have to be used at the gate as even if the APU wasn't operating we would connect the GPU while the aircraft engine was still running.

You should be able to start the APU using only the ground power. The battery is always on a standby mode incase of loss of power, I think.