An APU lacks the critical component that produces thrust, a propelling nozzle.
A propelling nozzle converts a gas turbine or gas generator into a jet engine.
Most modern passenger and military aircraft are powered by gas turbine engines, which are also called jet engines. There are several different types of gas turbine engines, but all turbine engines have some parts in common. All gas turbine engines have a nozzle to produce thrust, to conduct the exhaust gases back to the free stream, and to set the mass flow rate through the engine. The nozzle sits downstream of the power turbine. (NASA)
Would it be enough to keep flying an airplane if the main engines went out?
It would, in the sense that it will provide electrical and pneumatic power for the different aircraft systems, but no thrust. Or airplanes would have just been built with a few of those tiny APUs. :)
Another alternative for backup systems power when airborne is the Ram Air Turbine.
RE comment about turboprops having some exhaust thrust, they also have nozzles, which an APU still lacks. (NASA)
Before entering the nozzle (...) the exhaust velocity of the core is low and contributes little thrust because most of the energy of the core exhaust has gone into turning the drive shaft.