1935 GE Model A-53 AM/SW Tombstone Radio

[Electronic M]

It's possible. If you have swapped a second identical speaker and observed normal hum free opperation (which is what I think I read in your post) then you have confirmed something is not right with the first speaker.

What I would be looking at is the HUM BUCKING coil in the problem speaker. A large portion of electrodynamic (field coil type) speakers place a hum bucking coil in series with a lead of the voice coil. The hum bucking coil is typically a few turns on the same coil form as the field coil. The hum bucking coil acts like a secondary winding on a transformer formed by it and the field coil. The hum bucking coil picks up the AC hum in the field coil and feeds it into the voice coil 180 degrees out of phase. Ideally if the hum bucking has correct phase and amplitude it will perfectly cancell out any hum from the field coil so it doesn't produce audible sound.

If the hum bucking coil is connected with reverse phasing (read that polarity) instead of cancelling the hum it will double the hum (double the hum that would be there if you shorted the hum bucking coil or removed it from circuit which it's self would be worse hum than if the coil was working properly).

Also if the hum bucking coil, the voice coil or the audio output transformer secondary short to ground or B+ it could mess with hum bucking coil opperation.