The principle in 'Trompe' is applied to airplanes?
You are basically describing an ejector pump. This would not be very efficient, I'm afraid (I'll try to dig up some comparative figures).

The arrangement in this case would be a jet engine used to accelerate an amount of air inside a duct. With a long enough duct, the end result would be a single airmass exiting at (somewhat) uniform speed. Unfortunately, because energy must be conserved, the kinetic energy of the air exiting the apparatus would not even match the kinetic energy of the air exiting the jet engine, because of turbulence, skin friction of the duct etc.