Can a malfunctioning relay in an amp cause or allow a speaker to crackle when turning the vol potentiometer?
If you hear noise while turing a pot (for volume, eq, etc) in a traditional fully analog amp, then it's almost certainly a dud pot, and all you've done to try &amp; nurse it back to decent performance so far pretty much confirms this.  Replace it, and be happy :).  Ensure you replace it with the same resistance, and the same logarithmic type (not linear). (Or if it's under warranty just have the whole thing replaced!)

The relay protection is indeed to prevent 'turn-on pop/thump' as the amp's power-supply &amp; circuitry powers up, which can potentially damage speakers - it's a fairly common feature in traditional amps like this (except for amps designed by golden-eared monkey-beaters who'll claim it negatively impacts sound quality).  The signal from the amp to the speakers goes through the relay, such that the amp's signal either gets through the relay to the speakers, or doesn't go anywhere at all.  The coil of the relay is powered by the amp's power supply, but with a short delay of a few seconds to provide time for the amp circuitry to stabilise, &amp; disconnects immediately that it senses loss of power, too (some amps can put a decent whack of DC into the speaker as the power-supply fades).  This is highly unlikely to be the cause of your issues.