Without a schematic its hard to tell. But this transformer has nothing to do with the power supply.
I assume there's a small signal transformer after a gain (amplifier) stage that's being driven to saturation. The classic example of this is probably the
tycobrahe octavia circuit. More recently here we saw the same thing with the
Hudson Broadcast on this forum.
Basically, push a large enough AC signal through a transformer and it will distort/add/remove harmonics. I use passive DI's on keys on sound gigs to take advantage of this saturation. Makes a digital piano sound a bit more interesting