I don't question about your circuit or how it work, I only gives a straigth answer:
The transformer will not induce any current to a nearby PCB board by itself, given that the magnetic core is not broken (it need to be a complete magnetic circuit) and that the transformer does not run overloaded (I assume that a heavily overloaded where the core is way beyond saturated - the magnetic field may grow outside the core - but it will probably burn before that happens).
That is just me trying to say - it won't.
However - making an amplifier with a waste capacitor bank after the rectifier - wich is what I think you've done by looking at the picture, raises an issue - high current spikes will occur at transformer and rectifier. This might cause the transformer itself to make more noise/hum and the diodes might break down.
It could help to add an inductor right after the rectifier, but that might cause high voltage spikes when the current spike goes zero.