It should still work like that ,but even with resistances R1 and R2 both scaled back to 1/10 of the value you shouldnt cause any overload of the LT supply , as we said before the heater at switch on is 5-7.5 ohms , your voltage divider is 1260 ohms in parralel , lets calculate the extra current in the heater supply due to the voltage divider , 5mA extra , now try 96 and 30 ohms , now our potential divider draws an extra 50 mA from the heater circuit , thats not going to be an issue , a 6.3 volt indicator bulb would draw more current that that . The higher value of R2 will in itself cause a small voltage drop due to the cathode current of the tube which will offset the calculation to some degree , a lower value R2 sits the cathode closer to ground as far as AC signal is concerned , usually thats a good thing .
As was previously mentioned if you supply the cathode/heater in that way you may need an extra quiet 6.3v rail , the grid bias arrangement like the U67 allows extra passive smoothing of the grid reference voltage , likewise in U47 the 1780 ohm series resistor not only drops a lot of voltage but helps passive smooth the heater/cathode supply .
The NU67 psu spec says 6.5volts LT supply , To allow for some voltage drop in the cable the mic schematic shows between 5.7-6.3 volts , If I was to apply the voltage to the cathode Id favour the U47 type setup , if you want to apply negative volts to the grid just go with the standard U67 setup .