Can a fixed-wing plane jump up by blowing air over its wings?
As a partial answer to your question, air moving over a stationary (relative to the ground) wing will generate lift. There have been several weather related incidences where aircraft were picked up off the ground by significantly strong winds. Videos of these incidents showed that it was lift and not force from form drag that lifted the aircraft off the ground. In the case that the planes were tied down, they would come back down to earth in place. Unfortunately, the force of the decent, in some cases, was still enough to damage the planes.

I am uncertain about what you mean by “This would require that the lift generated would exceed ground friction reacting the propellor thrust...“. Lift would be acting roughly perpendicular to the wings chord line, and the plane’s longitudinal, and lateral axes. On the other hand, any friction created by the relative wind would be acting roughly parallel to the relative wind and the plane’s longitudinal axes. The only ground friction would be that caused by the wheels touching the ground. 

Thrust is a function of Newton’s Laws of Motion. The propellers turn chemical energy (in this case electrical energy) into thermal and mechanical energy. The mechanical energy is used to accelerate a mass of air. The mass of the air is accelerated by the propellers creating force. This force acts on the mass of the airplane to accelerate the airplane. The relative wind created by the propellers would act upon the airplane in the form of thrust and upon the wings to create lift regardless of how close to the ground the airplane was.

P.S.
Edited to include a new link pertinent to the discussion. Here is a new VTOL aircraft soon to be on the market.  

Blackfly