Take a look at this circuit diagram for my tube amp.
Even if you have no clue what you're looking at it's clear, at the bottom of the drawing, how all the tube heaters are totally separate from the rest of the amp circuit. You should also be able to see that the Power Light on mine is shown at the end of that chain. So if the power light is on, there IS power to the tube heaters.
However, the power light could be connected anywhere, if it were first in the chain then any break in the wires after that would turn off the tubes and the amp would be dead, but the power light would still be on.
Edit: The power light doesn't have to be part of the tube heater circuit at all.... it just happens to be in my amp.