I have never directly measured the 12v supply current. I did measure the AC power on the mains with a watt-meter one time. As I recall it was ~0.5W idle, and ~3 watts driving only one channel at 10v p2p sine into into a 50 ohm load.

Looking at it from a completely different angle: Its pretty easy to calculate worst-case power needed to drive the BNC outputs. I don't recommend actually doing this but... Assume we abuse the thing and make it drive +10V DC (open circuit), but short the BNC outputs with nothing but the FG's internal 50 ohm impedance to regulate the output current. That works out to 200mA of current, or 2 Watts per channel, times two channels = 4 Watts total. If we're not quite that abusive, and always use 50 ohm minimum load, then the max power needed by the output drivers drops from 2W per channel to 1W per channel = 2W total. Throw in another watt for losses, the FPGA, and the display and such, and you're back up to ~3W.

Im guessing a 5W transformer would be in the right ball park.