WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
Building, troubleshooting and testing of these amplifiers should only be
performed by someone who is thoroughly familiar with
the safety precautions around high voltages.
No, the VR tube keeps the voltage drop across it constant. If there's always (say) 100V between anode and cathode, as the anode moves up a volt, so does the cathode.