I too can replicate what the OP sees.
However, the same happens when you use several other effects:
Waves SSL Channel Strip, API-2500, PuigTec EQP1A and every other plug-in with an "Analog", "Noise" or "Mains/Hum" - switch I tested so far will show a peak value on the track,
if these switches are
on.
The track goes back to complete silence if these "analog" settings are
off.
Since the 1176 ProChannel module is modeled after analog hardware, the "noise" is probably part of the signal of the emulation.
IMHO not a bug, otherwise a lot of plug-ins would be buggy, too.