Turning on the DSP Engine switch does nothing whatsoever. It’s actually active in the off position–it’s a detail of the graphic design that we present it as turning something “on”.
In the off position, its behavior is a shortcut for flipping the enable switches on each of the sections in the DSP Engine to “off” if they are not already off. It does nothing extra. When “on” it has no effect at all–just the absence of forcibly turning that other stuff off.
But–if those switches are already off, then the DSP Engine switch truly does nothing at all.
All of that switch flipping happens before playback starts–once it’s running, the signal path is doing its thing, and not interacting with the switches in the user interface at all anymore.
I’m not sure what the cause is for the difference you’re hearing–but it isn’t the master switch on the DSP Engine.
Not doubting that you’ve heard something, but effects need causes that make technical sense. Before I explained this, you didn’t have the technical background in how that switch works to understand what its potential effects were–now you do. If I were you, I’d be looking for a more plausible root cause.