This is, oddly enough, still how many power supplies operate, but using electronic switches instead of a coil and a contactor.
Vacuum tube circuits use very high bias voltages (denoted by B+, usually at least 90 volts) to set up an electric field at the plate, which is controlled by a slightly negative voltage at the grid. The cathode in most radio tubes is a separate element that is more negative than the heater filament to keep noise from the electrical system from coupling into the radio by forming a reverse biased diode between the cathode and the filament. Some older types of tubes have directly heated cathodes that are not isolated. Since the filaments consume the most power in a tube circuit they are usually run directly off the battery (or electrical system) of the vehicle, and will pick up noise from the charging system and ignition system.
My old Fender guitar amp has a switch on the back that lets me flip the polarity of the heaters to select the less noisy mode.
If the radio was designed well it should work equally well with either polarity with the correct vibrator, but if it is not a good design it will be much noisier if run in reverse polarity. I don't have access to the schematic of your radio, so I couldn't tell you.
I've designed a couple of high gain tube circuits in my life and it can be pretty tough to make them quiet.
