At a constant power setting, does TAS change with altitude?
The answer to your question largely depends on what you mean by "constant throttle setting". 

For propeller propulsion, if "constant throttle setting" means "constant power setting" as in a fixed output BHP, TAS will increase almost linearly with altitude (up to the altitude where constant power output can no longer be maintained).

For a normally aspirated reciprocating engine with a fixed pitch propeller, a constant throttle position will mean a decreased manifold pressure with increased altitude resulting in less power output, less thrust (T), and thus decreasing TAS (assuming the decrease in thrust is larger than the decrease in drag (D) resulting from the decreased density at higher altitude, this generally holds true). For a supercharged engine, depending on how the supercharger is controlled, "constant throttle setting" can have the charge control maintain a constant manifold pressure. In this case, the power setting will be maintained (up to the maximum altitude where the supercharger can maintain the manifold pressure), and TAS will increase.  

For a jet propulsion engine, once again it depends on what is implied with "constant thrust setting". For example, for low/no bypass engines, a constant EPR should roughly correspond to constant T with altitude, hence with D decreasing with altitude, TAS will be higher before T = D. If "constant thrust" means "constant N1", thrust will actually decrease with altitude, how quickly it decreases with altitude will determine the effect on TAS (once again, where T = D).

If "constant throttle setting" simply implies "constant thrust". Resulting TAS will always be higher (as for a given TAS, T remains constant and D once again decreases).