That's a tricky question to answer but I would say yes: the hotter the heater gets, the higher its internal resistance rises (being SS the coef is positive) So if you hit the trigger without drawing, temperature will, rise, resistance will rise, voltage will then drop more across the load and Ohm's law tells us the amps will decrease, in turn lowering the power output.
Now if you remove enough of that heat by drawing, it will cool the heater a bit (good luck cooling it really though!
) and one could argue that it should allow to output more Watts and thus drain the battery quicker.
That effect would be with a stable voltage power source though. With our battery cells we have the voltage sag to take into account, and the sag will be lower when the load becomes lighter (due to higher resistance) so in some way it must counter-balance the above effect some...hm...