> output signal is half-wave rectified
Quasi-full-wave.
On sustained test tone, it will approach the peak-to-peak of the output wave.
On speech/music: it is unpredictable.
It will be 1.0-1.2V short due to Si diode drop. You need about a volt at the grid to get good GR. So the output will be a couple volts p-p while limiting, with nearly no GR for inputs up to 1 V p-p. That gives some threshold action.
0.7V RMS at the output needs about 10mV at the input at threshold, maybe 100mV in deep GR. Input level for SE 12AX7 has to be held to much less than 600mV for low distortion. It isn't in deep doo-doo, though it is too bent for "good" audio.
That assumes the rectifier pot is pretty full-up. If turned down, output level will be high, input level soon in excess of 600mV, signal grossly bent.
OTOH if pot is full up, the rectifier can be a heavy load on the cathode follower, clipping positive peaks.
Up to 1V of control voltage is applied to the grid which will amplify a thump. The cathode follower or a later stage will likely be thrown outside its linear range and clip for a while.
The attack is set both by the 5K/1uFd, and the 470K/0.1uFd in series with source impedance. If source is low-Z, it will be slow, OTOO 50mS. If source Z is much higher than 470K, it will be ~5mS but thump badly.
Oh: the 1.2V threshold is temperature sensitive, which might not be a problem though it is next to a hot bottle.
Build it, try it.