Assuming you mean Q from the series Star Trek: The Next Generation, I believe Q would be far more likely to bring George Washington himself to the ship. However, if only in possession of George Washington's underwear, then he would certainly use it to make a point about humanity to the crew, as well as use it to irritate Captain Picard (whom he has shown to have a long-standing interest in). Q would no doubt point out the irrational attachment that "puny humans" have to material possessions, especially those they attach historical significance to. He would likely make a game of destroying the underwear (perhaps by forcing the captain into a game by which he could save them), and in the end demonstrate that the destruction of George Washington's underwear has no affect upon history (or anything of significance). Q likes to comment on humanity, and thus the underwear would serve his purpose...with the addition of annoying the captain (which he also seems to enjoy).