Within the certification definition of Vmc then it would be incorrect to focus on induced drag and power. Vmc is defined at full power. Any reduction in drag would enable a faster climb out of ground effect (GE), thus it may only be a transient effect.
From a theoretical viewpoint the change in lift characteristics between the lower wing vs the higher wing (5 deg bank) in GE could change the lateral-directional control input required. Thus more or less aileron implies more or less rudder would be needed for directional control depending on aircraft design / configuration; there may be a similar change for rudder / tail plane effectives at small bank angles. Also there may be changes in prop swirl airflow or reflected thrust line for a jet that may change the control input required to balance the asymmetric forces. Whatever change there may be in thrust (thrust does not increase if drag reduces) it is the change in yaw moment that the thrust causes and the ability to control yaw, that are the important aspects.
From experience of Vmc tests at a safe altitude and separately establishing ground effects, I suspect that the net effect is to reduce Vmc. Some high wing aircraft, particularly with high tails show a double GE, indicating differences between wing and tail being in/out of GE. Thus there may well be a difference in down / up going wing. Low wing aircraft can also suffer from ‘bubble burst’ in GE which indicates a rapid loss of lift as speed decreases towards stall in GE, again indicating a change in the wing lift characteristic that may also apply to the aileron effectiveness.
For those concerned about control during takeoff and climb fear not: V2, may not be less than 110% Vmc. Vr may not be less than 105% of VMC; or the speed that allows reaching V2 before a height of 35 ft above the take-off surface. Extracts from JAR 25 Section 1 (FAR Similar).
Some references to asymmetric flight here:
http://uk.geocities.com/[email protected]/alf5071h.htm
See PSM+ICR and Asymmetric flight at low airspeed.
ALF