I would think it would use half the current running on 240 volts as it would on 120 volts because P=IV where P is power in watts, I is current in Amperes, and V is electromotive force in Volts. If V decreases, I must increase.
Indeed, but that's not what you wrote originally:
I would expect if it takes 0.2 amps at 100 volts, it would take 0.833 amps an 240 volts for the same output.
For 0.2 A @ 120 V, you would expect 0.1A @ 240 V.
Most of the USB chargers I have indeed state one current, but I do have one that does more: the Nikon
EH-69P has the following specs:
Input: 100V-240V~50/60Hz 0.068A-0.042A 6.8VA-10.08VA
Output: 5V=0.55A
My guess is that the mains current specified on the label is not the nominal current, but the inrush current, in other words: the current when plugging it into the mains, this will be higher but only for a short period of time.
To see if that assumption is true, I measured the nominal current from the mains at full output. I loaded the output with a DC-load set to 550 mA and measured the current from the mains.
At that load the current is 0.026 A @228.2 V. The apparant power drawn is 6.9 VA with a PF of 0.54 which equals to 3.8 W real power. So that's quite a bit lower than the spec would have you believe. That's why I think it's not nominal power but max power drawn only shortly as inrush current.
As an aside: efficiency of this AC/DC adapter is approx. 72%.