induced airflow

I have never quite understood indiced airflow. Suppose there is an
multi-engine airplane with wing mounted engines. I've been taught that
while the engine is running, there is a greater amount of airflow over
the wing behind the prop. The prop is throwing air back over the wing
which is creating more lift over that portion. If the engine were to
quit, that increased airflow ceases, and the wing is creating less
life, even thought the aircraft as a whole may not have lost any
airspeed.

Now imagine that same airplane had 50 engines on each side, totaling
100 engines total. Also imagine that the airfcraft is very very very
light, say 100 lbs gross takeoff. If that plane was doing a run-up with
all of it's 100 engines running full throttle (imagine this plane has
super neodymium coated brakes), the enduced airflow over the wings
would surely be enough to lift the plane right up, would it not?

Acording to the induced airflow principle, upward force is being
created by the airflow, is it not? Since very little force is needed to
lift this plane off the ground, it should take off. But common sense
tells us that it won't. Newton's first law says that for every action
there is a opposite and equal reaction. As the induced airflow pushes
up on the wing, it also pushes down on the engine, creating no net gain
in lift. Is my line of thinking correct here?