In USCF rated blitz tournaments, YES you can claim a win if the opponent leaves his king in check and presses the clock. It has happened plenty of times in my games. You can physically capture the king if you want or just claim a win.
Am I required to inform my opponent that I have him in "Check?"
Sort:
Under FIDE rules you are not allowed to capture the king in blitz but if your opponent makes an illegal move , in blitz , and you catch it you win the game , this is true on any illegal move not just leaving the king in check . I am not sure about uscf rules ...