Actually, the PT is not the source of anything. If it were, we wouldn't need the power company or batteries. We could power everything with transformers! Batteries or solar cells, etc., can power amps; but for our purposes all power comes from the Power Company, through your wall outlet, through the PT and through the tubes.
Per Ohm's Law, a resistor in series in a circuit does 2 things simultaneously: it drops voltage and limits current. A tube rectifier has more resistance (though here we call it impedance due to the presence of AC current) than does a SS rectifier. Hence, a tube rectifier will drop more voltage and limit more current than does a SS rectifier (which drops only about 1V).
With less B+ on the plate, the tube will draw less current - all other things being equal. But we can make a tube draw more current, at lower voltage, by biasing it hotter.
We can pull as much current as we want, from -0- to infinity (and beyond, for Buzz Lightyear). If we substitute the load of the tube with a short circuit we can in theory pull an infinite amount of current through the PT and the rectifier. But if we allow more current to be pulled than the fuses, wires or components can handle, they may be damaged or fail.
Whatever current anything draws, it draws from the Power Company (or some other actual source of Power).