Voidugu:
The atmega, opamps, display etc would't have any problem since they would be powered by a voltage regulator (probably a switching voltage regulator). My concern as i said before is the reliability of the heater of the iron under such conditions.
Well do what you wish, but your kind of on your own. I have a Weller soldering station of probably the same wattage range and it heats up in maybe 10-15 seconds, so I would see no need to try and make it faster.
Lefty