Nick, it is my understanding that if you’re talking about balanced connections and external interference introduced to the cable from amp to headphone, then no, it does not inherently cancel emi. For noise introduced into the signal from the DA conversion process itself, interference or mains hum introduced to the amp circuits, tube ringing, etc… still no.
Noise generated by the components can just become part of the signal, unfortunately. So if your tube rings, or if mains noise from the amp is getting into the signal, or if your DAC just sucks and noise is getting into the signal and passed along to the amp, then any amplification that happens to that generated signal will just get amplified as well. (Unless the designer of the amp went to elaborate lengths to design noise filtration into the amp, that is. Which is entirely possible.)
BUT… For signal transfer from DAC to amp, yes, balanced will cancel noise. (Unless the amp manufacturer cheats, ties the ground and - wires together, and only uses the + wire to pass the signal. In which case, you basically have a really expensive and crappy 3 wire RCA cable. Anyway, I digress…)
Signal:
Balanced going from DAC to amp has 3 wires (per channel). It has: +, -, and ground. The + wire has the normal signal, - has an inverted signal, and ground is ground. A clean signal on these wires looks like this (+ on top, - on bottom):
When noise from EMI/RFI is introduced to the wires, it could look like distortions in the sine wave, like the black lines (messily) show:
When the signal gets to the amplifier, the - signal is inverted and summed against the + signal. Like such:
The black peaks cancel each other out, leaving us with a sine wave that is twice the strength of the 2 signals.
Amplifier:
Going from the XLR connection on the front of the amp to your transducers, the headphone is incapable of performing the inversion of the - signal, summing of that signal, and thus… no cancellation of interference. In fact, if you were to send a sine wave and inverted sine wave down the + and - connections to your headphones, you would end up with a zero volt signal at all times, and no sound would come out at all. So, if the + and - wires of one transducer receives this:
… It is going to reproduce exactly that, red bumps and all.
What XLR connectors do allow are for are 4 dedicated wires, 2 of which go to each transducer. This means that in a truly balanced & differential topology, each + and - wire can have it’s own amplifier.
Sometimes the XLR connection is just there for convenience, and the internal topology is actually single ended.
And, of course, the TRS connection just joins the grounds at the plug:
IMO, the one of the biggest benefits of using XLR connections for headphones - besides being able to use fully differential amplification - is that the connection does not short amplification circuits as it’s being connected, very much UNLIKE 1/4" TRS jacks where the left + and right + briefly get shorted to each other as the plug is pulled or inserted, and which I assume is why Phonitor amps release the magic smoke if the output is not muted first.
I hope that helps.
(Images created at https://www.desmos.com/calculator and https://www.circuit-diagram.org/editor/)