Will creating a strong back pressure within a ducted propeller enable an aircraft to attain a higher altitude?
A very creative thought and project - a centrifugal compressor could be used as a means of propulsion if the exhaust stream is properly nozzled. So what you're basically doing is switching on another engine to produce more thrust, but:


The extra engine is in the way of the propeller, blocking its outlet flow. 
Propellers and rotors are very efficient thrust generators on their own.
Creating static pressure is not the most effective way of creating thrust, better to convert it into air flow velocity. 


Anything that is in the way of air flow creates back pressure and/or friction. The propeller flow is blocked, and the compressor flow runs into the side wall and does not accelerate any air backwards.

The way the air from the centrifugal compressor is normally deflected is depicted below (from an old uni book). 



Air flow needs to flow and be guided gently. If it hits an obstruction, it pushes against it and creates negative thrust, like a person in a sailboat pushing against the mast.

It won't fly, I'm afraid...

Starting an extra engine might help in reaching places that are hard to get to. A simple propeller or turbofan is best - but when the extra propulsion is off, it is dead weight. Best to crank up the engines that are there already.