May or may not. It depends on the configuration of the LNA.
If LNA has been configured to achieve "Minimum Noise Figure", there is probably a Frequency Selective Network and/or a Narrowband Matching Circuit to achieve Minimum Noise Figure. Therefore, 100GHz with +20dBm Power Level can-perhaps-not enter directly into the circuit but it may create a perturbation as EMI.( due to weak shielding etc.) Additional to this, 100GHz is probably far beyond in term of fT for the LNA transistor.
Nevertheless, the LNA must be shielded and a SAW filter must be placed because there are other strong interferences out of 100GHz.
If the LNA was designed for 1.6GHz and the interference is 60 times higher in frequency, most probably the LNA will be totally insensitive to that interferer.
the gain of a 2 ghz amplifier at 100 ghz would probably be -60 db. so....there is no chance the output of that amplifier would be anywhere near saturation. In fact, when i say gain, i probably mean more "leakage" from input to output.
there is a slight chance a 20 dbm signal at the input might move the dc bias point around, but that is a long shot too.
if you want to be sure, add a simple lowpass filter to the input, like a mini circuits chip lpf