Even if Shakespeare knew little of the structures of melody and harmony, not to suggest that was the case, his mastery of verse form should assure us that he would not lose time when hearing sung verse.

He kept a sense of humor about it all, obviously, and I imagine that he might have found serious analysis of his comic wordplay amusing. There's a line of a BeeGee's song that I'll pull way out of context; it is, I believe, "Ah, but I didn't see that the joke was on me."