"The electrical hydraulic pump on No.4 System can only be driven by AC power and not off of the batteries then?"
This is correct, but, as mentioned, the electrical hydraulic pump may be limited to ground use only anyway. Some 747-400's have electrical auxilliary hydraulic pumps on both the #1 and #4 systems. They have a lower output than your Engine pumps, Air-Driven Pumps and AC Motor pumps, but are useful for pushbacks and aircraft maintenance.
The only source of AC power with the engine generators out of commission is the battery-driven Static Inverter. This is a solid state device and wouldn't have the power to drive an electrically driven hydraulic pump.
Rgds.
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