Low Probability of Intercept radios can be harder to pick up because they use various techniques like frequency hopping but even then they don't blend in to the background.
see https://www.itu.int/itunews/manager/display.asp?lang=en&year...
To this extent, there are methods to reliably detect signals 12dB under the noise floor, and as I said this is an area of active research and militaries are probably even further ahead.
Though, if I am not mistaken, the laws of super-sampling hold in this case, and SNR is only improved by O(sqrt(N)) for N samples, so this approach will have practical limits as one has to place a very large number of receivers in range of the emitter (or do auto-correlations over a very long time window), with enough separation to make sure the noise isn't correlated anymore, if looking for a signal deep below the noise floor.
Consider how unsophisticated the Enigma machine looks to modern eyes. Now throw some modern encrypted traffic back at them, would they even understand there's signal in there? Unlikely.
Those are just few decades of difference on the same species with the same tech history.
Definitely yeah
To address your other points,
"Consider how unsophisticated the Enigma machine looks to modern eyes. Now throw some modern encrypted traffic back at them, would they even understand there's signal in there? Unlikely."
Depending on how far you go back yes they would. Most communications today happens in the same frequency ranges they did decades ago. UHF is UHF.
You bring up Enigma. I'm confident if Alan Turing were scanning the airwaves and heard a modern encrypted radio transmission he would immediately determine it was man made and some type of communication. He wouldn't have any hope of decrypting the signal or analyzing the packet structure. The mathematical theory behind modern encryption didn't exist yet let alone the compute power needed to crack it.
"Knowing the popular protocols is an advantage you wouldn't have with "alien communication"."
Normally projects like SETI will look for patterns and structure in the signals they detect. Nature can create some very complex transmissions and it can also create some very regular ones that are simple. But you rarely see both complexity and structure in a signal that isn't man made.