This is a great triva question and I would love to see some real figures on different types just for fun. Surely the contribution of running the APU at take off would be to remove the aircraft's electrical load from the main engines, as opposed to actually contribute to propulsive thrust from the gas exhaust from the APU?
If not, then if I imagine that the residual output from the APU did have a non-trivial effect on aircraft thrust, then what would I do to increase this residual thrust? I would dump more (electrical) load on the APU in order to increase the fuel burn required to keep it running and hence get myself more residual thrust o/p as a result.
Following this (il)logic then requires that in order to increase the APU thrust you switch on as much electrical equipment as possible!! (assuming this does not of course degrade the o/p of the main engines).
Anyone got any concrete figures?