the bypass cap DOES affect the gain, but it does something else
too, which ray hinted at: it adds a time constant to the cathode
circuit. that's nothing more than a fancy way of saying that the
cathode circuit, with bypass cap, has a sort of "memory" to it... the
voltage across the cap will be affected not only by the signal that is
instantaneously entering the stage, but also by the signal that just
WENT THROUGH the stage.

when you overdrive a typical gain stage hard, you increase the
average cathode current which passes through the valve. when this
cathode current is drawn through the cathode resistor, it ends up
increasing the voltage drop across said resistor. the cap will resist
this change in voltage, instead sinking current in a valiant attempt to
keep the voltage across it stable. this can only go on so long. if this
increased plate current is kept up, eventually the cap will rest at a
higher voltage than before... and it will resist any FURTHER
changes in voltage, even if the signal is suddenly stopped. a finite
time must pass (the time constant) before the cathode returns to its
normal quiescent state. this can be--and usually IS--audible, and i
don't care for it much.

of course with smaller bypass caps this effect is much quicker to
come and go, so the ultimate result may not be that displeasing. this
is part of the reason why marshalls sound so much better than
fenders when you really run 'em wide open... they use smaller
bypass caps, in general.

there is also the effect of the cathode bypass cap increasing the
likelihood of grid blocking distortion, which i think ray also pointed
out. to get a feel for this, imagine an UNBYPASSED gain stage.

to some degree, an unbypassed cathode (or a cathode
degenerative gain stage, as they are more precisely known) is sort
of like a cathode follower, in that the cathode will tend to follow the
voltage on the grid. if the grid voltage swings positive, then so will
the cathode, and vice versa. there is a natural tendency to avoid the
conditions required for grid conduction (the cause of grid
blocking)--namely when the grid becomes more positive than the
cathode. this is seen to great effect on many of mike soldano's
designs, like the slo, where he uses a very high unbypassed cathode
resistance on a plate loaded stage... something like 39k. there really
isn't much chance of making that stage fart out, because of all the
degeneration going on across the cathode resistance.

now, add a bypass cap, and the cathode is held (to a varying
degree, as discussed above) to a fixed potential. the grid may swing
positive, but the cathode bypass cap will sink current, stabilizing the
cathode's potential. clearly the point at which the grid's potential
exceeds the cathode's will appear at smaller input voltages. that
point marks the onset of grid clamping. 

of course, there's also higher CURRENT swings through the tube,
since the cathode is not degenerated and the effective Vgk swing
has been increased, so that usually results in more single stage gain.
that's essentially why you'd use a bypassed cathode, for an increase
in single stage gain. there is also a noise benefit (there's less with a
well-bypassed cathode) and an output impedance benefit (it's
lower with the bypass). there's more than that to good tone,
naturally.

i have had great success in gonzo overdrive levels by reducing
circuit impedances to make the time constants faster. this goes for
most of the grid circuits, like grid stoppers (i actually don't use 'em),
grid leak resistors, and increasing cathode resistance values. of
course, no bypass caps, if i can get away with it. when i do use
them, it's usually in stages that do NOT clip at the grid, or they are
of low value. then you can cascade say 3 stages and get total
rippin' distortion.

i could talk more about this, but i'm also sipping a tom collins. i
know i didn't directly answer your original question, but i may have
answered some others you didn't ask yet.

ken

Punch in some numbers, clip in some caps, see how it sounds!
Also, an unbypassed stage (an Ampeg favorite) may have a sound
you like, too.

The famous Marshall/tweed Bassman stage would be:

1 / 6.28 x (2700 x .6) x .00000068 = about 145 Hz