It would be rare I think. Shutting down #2 engine for taxi with no APU is normal ops. It's done on most arrivals where there's time to cool down and shut down. (2 min cool down)
Having said that, I've seen on rare occasion where when a power source comes on / off line a bunch of electrically based EICAS messages appear with audible warnings which I guess could be a distraction.
Hyd 2 controls the nose wheel steering. When on the ground with engine #1 running and brake is released, the AC pump would be on (system logic, assuming the switch is in auto which is normal). It's powered by AC bus 1 so it is already running. If there was a momentary loss of electrical power, I would think the accumulator should give enough pressure to steer.
Also, half the brakes are on Hyd1 (inside? / outside? I forget) whose pump is running, and there's always the parking/e brake.
The warnings clear within a minute. In 3 years I may have seen this maybe 3-4 times. In the two times it happened moving, it did not cause a loss of brakes.
But not having been there, who knows.