re: "Are you planning to stand on this box after it is mounted on the wall or something ?"
I have some extension cords and tool plugs that require a decent amount of force to remove from the receptacle. By "a decent amount" I mean more than a couple of (or even four) plastic anchors in 1/2 stucco could withstand for very long.
That's why we're suggesting screws that reach the sheathing or a stud or maybe even molly bolts.