Maybe I shouldnt have said "Fuzz Face type circuit", as the Fuzz Factory isn't based on any old design. In something like the Fuzz Factory, though, it works well. That would be an interesting experiment to try it on a Fuzz Face circuit.
Quoting Paul Perry:
"Some amplifiers will oscillate when there is resistance in the power supply, because of positive feedback. Where does this come from? The first time I saw this, it was a two transistor amplifier, where the current drain through the power supply resistance caused the voltage at the amplifier power input to ripple in sympathy. And, depending on the design of the circuit, this ripple can get to the input stage & if it is the right phase there, cause feedback. Note that the effect can be present without being strong enough to cause oscillation, in which case you wonder why none of the maths work!! Too much gain, input impedance nothing like you expected etc.
And that is why a "flat" battery can make a different sound (as well of course as the voltage being lower)."
All that to say that it may work on a Fuzz Face circuit.