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I had to revisit this today.

E+ never even calculates impeller efficiency explicitly.

It calculates fan power (Ptot) as static pressure * volumetric flow rate / fan total efficiency.

The Design Heat Gain of the fan is calculated as

Source: Engineering Reference Design Fan Heat

This can be seen for eg for the FanVariableVolume here: Fans.cc#L1801-L1804

If you start playing around with the equation and trying to reduce/express it differently, you'll notice that

given that total_efficiency = motor_efficiency * impeller_efficiency (I'm calling Ptot = Pfan,des)

Pshaft = motor_efficiency * Ptot = total_efficiency / impeller_efficiency *  DeltaP * V_dot / total_efficiency
       = DeltaP * V_dot / impeller_efficiency

Makes sense.

Fan heat gain is then:

Q_dot_fan_heat = Pshaft + (Ptot - Pshaft) * motorInAirFrac.

In other words, the fan heat gain is the sum of

• The mechanical energy delivered
• The motor inefficiency x the motor in AirStream fraction

If your motor in air stream fraction is 1, then no matter what you put in the "Motor Efficiency" field, you'll always have the same values.