If the hat was extremely porous, yes, this will work to a degree. But if it's not, it will be quite muffled.
Overall, you can put a mic anywhere on the body and get some kind of pickup. The question is, do you want it clear and present, or muffled and distant? This is the kind of thing you test a few days before the shoot. Going out on a shoot with the idea of "I'm going to do this" without having tested it previously is crazy. Just the variables of the location are bad enough without knowing the specifics of the placement. Even small things like testing a mic in a warm living room or office will be thrown when you move to an outdoor alleyway in cold weather or early in the morning.

The characters are wearing turtlenecks and such so I was unable to use a buttonhole but I pinned the lavs about an inch above nipple level on top of the sweater and placed a very light scarf over them, secured the scarf so it wouldn't rustle and it actually sounded better than when it was exposed directly, I guess the thin scarf acted as kind of a windguard or something.