I saw this same question in the Spirit board, but didn't read it.

From personal experience, I'd have to say that's a strong "Maybe." It really depends on the GA you're dealing with, whether F9 is incentivizing them to sell carry-ons, how much they need that extra money, if they're having a bad day, and so on. Flying out of MCO, I once saw a F9 GA tell someone their bag of fast food was a "personal item" and they'd have to pay to take both it and their actual bag. It's not a big jump from there to the Yeti, so--while I personally feel it's unlikely--it very well could.