Is it? It might be. I feel like there's a perfectly legitimate joke to be made saying "I'll wear a morning coat!", the humor drawn from the antiquation and over-the-top nature of the suggestion, rather than the fact that it describes a style of dress that has always been for a different type of situation.

In fact, I think the structure of that joke ("I'm doing what you said, too hard") is a better one than the structure of the joke you imply, though the joke loses something in the current environment of general unfamiliarity with morning dress...