Very interesting question.
Technically it is possible and relatively easy. We can just connect some sensitive microphone. From the output we can make frequency analysis in real time and here we can obtain interesting frequencies. We can then know which tone may be related with LENR. My opinion is that we will not hear anything except heater.
But the problem is, that we don't know frequency range. But the biggest problem is, we have succeed in the replication first.
By the way I think that gas e-cat and hot-cat are very similar. Here the target is same but there is little different way to achieve it.
I think that hydrogen and nickel must be present in the system all the time in some form.