Not necessarily. There are plenty of games that have had "joke characters" that are perfectly viable and are just really stupid in concept - pretty much all the animal characters in Tekken are like this. "Dan Hibiki" is not the only variety of joke character; making a character intentionally bad is just one of the (in my opinion, less fun) ways of foisting that title onto them.
No, Dan Hibiki is actually what a Joke Character is. The only other variety is one who was supposed to be a joke, but turns out amazingly good(like Jigglypuff in the first game. And kind of in a later game, but I forget if she's good in Ultimate?). They're called Lethal Joke Characters.
You're probably thinking of Comic Relief, which has nothing to really do with a Joke Character at all. They however do related to the Fighting Clown, which is directly what Wii Fit Trainer falls under. She's not there for Comic Relief, mind you, but the idea of her is very silly.
Overall, all three terms mean highly different things. Wii Fit Trainer is absolutely a serious addition to the roster. There's no joke being made by adding her. Her playstyle however is still ridiculous, which is why she fits Fighting Clown(which is for characters who are silly in appearance but actually aren't terrible in gameplay, sometimes really damn good). Others included are Villager, Piranha Plant, Isabelle, and Duck Hunt, to name a few. Though this also applies to Mr. Game & Watch, Luigi(he's meant to be klutz), Wario(that janky movement is beyond silly), and Steve/Alex.
Either way, you're not talking about the same thing as an actual Joke Character in this case. Just a Fighting Clown, Comic Relief, or at best, both.