Can you hit a goalie in the NHL?

No, skaters cannot intentionally cover the puck or else it's a 2:00 delay of game penalty against the player.

If the puck is covered by a skater in the crease, a penalty shot is awarded to the opposing team. The crease is the painted area in front of the goal, and that area extends upward from the ice surface up to infinity. (Think of a half cylinder extending upwards from the ice.) If a defending skater cups his hand around the puck or otherwise covers it while in this "half cylinder" a penalty shot is awarded. The puck does not have to be touching the ice.