Yes. There are several instances throughout the series where you can see Mario sleep. In the main series 3D platformers, if you wait long enough without doing anything, Mario will fall asleep. In Super Mario RPG Legend of the Seven Stars and in the Paper Mario Series (excluding Sticker Star) you can sleep in inns. It's also the same deal as the 3D platformers as you can fall asleep by waiting long enough. There are also humorous instances where Mario will fall asleep when someone is talking for a long time. In Mario and Luigi Dream Team, during the final Antasma fight, Mario has a chance of falling asleep if he gets hit by one of Antasma's attacks.