I don't know how heaters can be "noisy".
The way we usually FEED them can be HUMMY, cuz we use AC.
This amp avoids that. The 6L6 cathode current is fairly well filtered DC. From the heater point of view, it is a "cathode follower" with kinda-nasty on the plate, better-filtered on the Screens, and dead-ground on the grid. The cathode "follows" the sum: mostly G1, about 5% of G2 jiggle, and maybe 1% of plate jiggle. There's probably less than 0.1V of ripple at the cathodes.
Hiss-noise? All resistors do. But Pure Metal (Tungsten) much less than Carbon Comp, even less than Carbon Film, which we have all over. Also the voltage/current ratio of the hiss source goes by resistance. The heater is about 84 Ohms, which is much lower than any resistor in our hiss-critical stages (or the guitar self-resistance). And as HBP says, here injected into the highest-level stage. True, hiss also goes by Temperature, and the heater is by-far the hottest resistor around (except a pilot-lamp). Doing math we have maybe 0.03 microVolts of hiss across the resistor. Compare to the 0.6uV across that unbypassed 2.2K cathode resistor, or the 1uV-2uV of a clean 12AX7. It's nothing.
Also, hiss injected push-push at the cathodes will tend to cancel in the push-pull plates.
The "sweetest" hi-fi I ever met was a Fisher Console which used this exact trick on the preamp tubes, only using four 6V6 for the power stage.
The main drawback is that the rig takes TWICE as long to come to life. First the big bottles have to warm enough to flow cathode current. Then the preamp tubes *start* to heat. Net result is about ~~20 seconds before the first note comes through. Unless you are running a snack-bar call-system, that's a reasonable exchange for very quiet preamp heat without modern high-current rectifiers or added giant caps.
A side drawback is that a "dead output stage" can really be a broken preamp heater, perhaps perplexing. However a serious search for the big cathode resistor will lead to the trick and an easy try-this (change preamp tubes).
This amp shows 10.25V on the "12.6V" heaters. But note that in large-signal work the 6L6 will shift up in current, maybe 10%. Note that Dynaco ran their preamp tubes on 10.5V and sound OK. The 12AX7 uses the same heater/cathode scale as 12AT7 and 12AU7, but never passes even 1/3rd of the current that its sisters can. Moderate under-heating seems to not be a problem.