I build+fly small RC quadcopters, and I've got a couple of small RC helis, too. And I can't see any way that a heli or quad will ever fly from pure Lego :(
A helicopter rotor head is way too complicated (and needs to operate at very high speeds), and to control a heli, the minimum you'll need is two motors (main and tail) and two servos to control the rotor head.
Quads are much simpler mechanically, but still need to be light, and have a lot of motor power for their weight, as well as a controller board with accelerometer/gyros to stabilize them. An NXT could probably do that, but they weight rather a lot...
Your best option is probably to build a quad using a Lego frame, and proper RC gear (RX, motors, ESCs, props, control board), but disguised as Lego. Maybe you could even control it with an NXT, and modify the NXT to conceal a LiPo battery? Not sure if an NXT could drive ESCs though. Maybe you could use the shell from a dead NXT, and squeeze in a battery and KK2 flight controller (http://www.hobbyking...trol_Board.html)? Maybe even mount your brushless motors in PF motor casings?...
At least a couple of people have built Lego frames for RC quadcopters, but I've not seen anyone try to make one that looks like an actual 'Lego Quadcopter' though...