Sure! But note I said "initial intuition". return/pure and monad laws can be explained later, once one understands that there's really nothing magical about monads.
Of course there's nothing magic. But I think it's important to grasp the definition as a whole rather than thinking monads are "just" some subset or superset - the full definition of a monad is quite short and every part of it is vital, even if it doesn't seem so to start with.