Mythbusters did an episode about this. If I recall correctly, they made the two hosts up with Hollywood-style prosthetics to look like each other and had unsuspecting test subjects who were familiar with the show interact with them (at a distance) to see if they noticed anything amiss.
The results were mixed.
Hey, they don't call it the Impossible Mission Force for nothin'...
Remember the 'masks' in the first couple Tom Cruise MI flicks? Geezus, did they GROW them or something? The effect of pulling them off was done very quickly, and that was smart, because if they'd dwelt on it at all, I think the whole theater would have been rolling eyes, but as is, it gets by, even though it seems about as futuristic fantastic to me as warp drive.