A correctly calibrated APPS will make the engine run smoother and more efficiently than an out of spec APPS.
I can see a new APPS producing those results over an old APPS with dirty or worn brushes, but I don't see how adjusting the voltage will change how the engine runs. The ECM translates the output voltage of the APPS to a desired RPM - nothing more. And the ECM self-adjusts for the voltage range of the APPS.
So let's say that you're tag says . 550v and your actual reading is . 500v. According to the "calibration" procedures, you advance the APPS rehostat body so the actual volts match the tag at idle. You've simply moved the brushes further down the plate by a degree or so. Effectively the same thing as depressing the throttle pedal a touch. And Pushing on the pedal a little bit won't make the engine run any better, just a little faster.
After reclocking the APPS rehostat, the ECM needs to learn the new minimum and maximum voltages from the APPS so it can assign them to idle and full throttle, respectively (disconnect/reconnect batteries, key on, pedal slowly to floor and back to idle). Before the APPS adjust, 1. 00v might have resulted in 1,500 rpm no-load (made up numbers just for example). Now, after reclocking and re-teaching the ECM, 1. 05v would give 1,500 rpm. Engine-wise, that is the only thing that has changed. Timing and fueling are based on intake temperature and pressure, and engine load. The APPS voltage/rpm relationship is irrelivant to engine performance.
Where this can help however, is the case where the few degrees of twist might put you past a bad spot on the brushes. Since the bad spot usually happens at 1,800 +/- rpm though, getting past the bad spot is unlikely. The folks most likely to benefit from the adjustment are the auto trans guys, since adjusting the volts to match will get the auto transmission shifting to match the engine load more precisely (like Jeff).
As an example of how the voltages don't effect the manual transmission trucks, I replaced my factory APPS (. 520-ish) with a Williams Controlls APPS (. 640v) and didn't notice a thing (aside from the missing dead spot). If idle voltage was worth anything more to the ECM than an RPM command, I would have surely noticed something with that big of a jump.