No, DMX is a hf signal, waaay above the audio frequency range. It would not pass because the system’s frequency range has to be limited in order to be processed by the mixer.
This is not like a hardwired connection.
Most Intercom signals also contain a DC signal on top of the audio, used for call signals.
That would be blocked, too.
If you take a look inside a cat5 multicable, you’ll always find one or two real DMX cables besides the cat5 and the AC cable just for these kinds of signals.
A real copper cable connection can’t be beat for these purposes…