Balanced will reduce noise (in terms of RF noise, of course) significantly better than unbalanced,
In this situation I don't think it will at all.
I don't think that balanced vs unbalanced is actually electromagnetically that different in this particular configuration (see my edit at the end of above). Things like where the wire is sitting on your body and what pose you are in will probably affect RF noise pickup levels on the headphone wires much more than changing between bal & unbal signalling.
but the source of noise does need to be far enough away from the capturing device to not affect it directly and, therefore, be able to be negated by the balanced cable.
I didn't get into near-field and far-field effects. I'm not sure that it really matters here, but I might be wrong.