Power Source for Standby HYD PUMP B737
 

As long as the engines are windmilling (sufficient airspeed and no severe damage), there should be enough pressure from both EDPs to have normal flight controls.

Standby pump is powered by AC transfer bus 2, so that won't be available in your scenario.

Thanks Flying Stone. The background of the question was related to the rudder, which will get harder to use, as we slow down with no standby system.

I think the rudder will be the least of your problems in this scenario... After all the main reason you would need the rudder on large aircraft would be to compensate for an engine failure :}

further…
 

The pump pressure switch closes and supplies a ground when the EMDP pressure decreases to less than 1300 psi.
The STANDBY HYD LOW PRESSURE amber light comes on when pressure decreases and one of these conditions occur:
• Either FLT CONTROL switch is in the STBY RUD position
• Auto standby system relay is energized
• ALTERNATE FLAPS arm switch is in the ARM position.
The ground from the pressure switch also causes the MASTER CAUTION light and FLT CONT light on the system annunciator panel to come on. These lights come on when any of the amber lights on the flight control panel come on.
The STANDBY HYD LOW PRESSURE light, the MASTER CAUTION light and the FLT CONT light go off when the EMDP pressure increases to more than 1600 psi.
The ground from the pressure switch also sends a signal to the flight data acquisition unit (FDAU).
See the Flight Data Recording System (FDRS) section for more information on the flight data acquisition unit. (SECTION 31-31)