Inductor Fed VR Tube
There is nothing wrong with your relay coil proposal BUT if your power source is a 50Hz transformer single phase full wave rectifier then most of the power supply noise will be 

100 or 120 HZ so millihenries wont do it   in fact you want henries to achieve anything In the old days before I was born high inductance filter chokes were common but nowdays capacitors are generaly much smaller cheaper and easier to find