I saw Kaufman once at a club in LA. He did his Foreign Guy for most of the show, doing some of the most awful impressions you'd ever seen. As it went along, people started to get restless... he was getting heckled, etc. And yet, he never broke character. Then, his last impression was Elvis, and it was dead-on perfect. Kaufman probably did Elvis better than anyone. That's when everyone realized the joke was actually on them, and the place erupted in laughter.
BTW, if you ever go to the Jerry's in Studio City, they still have the picture of Andy working as a busboy (which he did, unbelievably, while he was starring in Taxi).
If anyone could pull a stunt like this, it would be Andy (though I doubt it's true).