According to this
http://www.radiostation.ru/tubes/6SN7.pdf
They are both 3.78 watts; 6SN7 draws 600mA at 6V, 12SN7 draws 300 mA at 12 V.
So the answer generally is no. In a parallel circuit, it will draw double current at 12 volts and burn out. In a series circuit, it will decrease the total resistance so that the string draws somewhat more than 300 mA, but this will still be too little for the 6SN7.