Yes, that's how it works. I'll provide a link. If an amplifier is correctly designed, "sagging capacitors" amounts to a cable marketing blurb. If you think any substantial amount of juice for your volume control is coming directly from the cable you paid a lot of $ for then you're not following the design topology and you're listening to music with your wallet.
http://www.radio-electronics.com/info/power-management/linear-power-supply-psu/basics-tutorial.php
http://www.radio-electronics.com/info/power-management/linear-power-supply-psu/basics-tutorial.php