Dick,
I agree with what has been said above. Downwash from the flaps, or any other aerodynamic influence, cannot vary the angle of fully powered flying controls (unless PFCU jack stalling occurs). Normally, the controls would be designed such that the elevator is in line with the tailplane when trimmed as this is the minimum drag condition for balanced flight. It sounds like the B737 fuctioning that mono describes was a fix to increase pitch trim authority without increasing overall tailplane deflection (or to maintain trim authority whilst reducing tailplane deflection). It is feasible that an automatic trim input could be designed into an aircraft for when, say, the flaps were lowered, but I would imagine that this would deflect the tailplane and not the elevator.
The BAC 1-11 also has a tab on the elevator for trimming when in manual following a double hydraulic failure.