The Blue Pump is available when
1)there is AC power (not just Battery) with or without engines running in flight, and
2) AC power avail and one engine running on the ground.
3) There is also a Blue Pump Override switch which will force it to on regarless
The RAT extends on loss of both AC Busses and will pressurize the Blue system to 2500 psi(I think, cant look it up now)
The RAT does not have its own Generator and hence does not Provide AC power directly. AC Power is provided by an Emergency Generator running off the Blue Hyd system.
If your RAT stalls (at 100 kt, I seem to recall), the Batteries will power the AC busses via the static inverters. The AC SHED DSS and DC SHED DSS busses are .. well.. shed.
I really dont know how long your bats will last in this configuration..
Cheers, and good luck to you.
OORW