Well these guys do it. It's pretty funny.
They all keep straight faces and there's a video of their exploits.
Improv Everywhere has a bunch of other "missions" they undertake. One of the coolest is when they descend on a normal little league game with a crowd of fans for both teams, real NBC announcers, a jumbotron, mascots and the flippin' Goodyear blimp. The players and coaches and families were not in on the joke, they merely get the best game ever.