I think you're asking the question probably because some other aircraft types, their EMDP only kicks in (comes on automatically) under certain conditions, normally when load on hydraulics is high such as when flaps or landing gears are operated, or if hydraulic pressure drops to a certain value (maybe due to EDP failure),
At other times the EMDP is automatically off, only EDP is on.
On these aircraft, the switches for the EMDP are most likely labelled OFF, AUTO or ON. The normal position for the switch is AUTO. ON is to force the EMDP to run.
So yes, to answer your question with regards to 737, the EMDP is always on, and so is the EDP when the engine runs.