Nope - or at least I can't hear any hum. Might it make a subtle audible difference? Dunno. But since it's easy and cheap, why not try to get the stuff that you don't want to produce signal to be as quiet as reasonably possible? For my Kaiju rebuild, I will be experimenting with a solid state HV regulator [edit: so that the B+ feeding the output stage is also regulated]. The designer reported a max of 300 uV output noise, but almost all of that was residual ripple passed through by the reg. Looking at his output noise plots, by my eyeball estimate the intrinsic noise output of the reg, when mains ripple is removed, is about 3 uV. So I am aiming to have minuscule ripple going into the reg via a CLCLC filter comprising doubler, 10H/200mA choke, 200 uF high ripple voltage rated film cap (huge! 25 cm long!), 10H/200mA choke, 1500 uF film cap (also huge, but mostly diameter-wise). Overkill? Absolutely. Fun factor: off the charts. Plus, I think the giant aluminum can film caps will look cool on an all aluminum chassis alongside the new big black MM output transformers.
cheers and thanks, Derek