No, I wouldn’t recommend that. Doing so would come across as you thinking they’re untrustworthy. In other words, go ahead and do this if you want to squelch your chances of them hiring you. If they do use what you’ve done without hiring you, well, it might be highly irritating, but so what? It’s not like you’d really be out anything at that point.
I don’t agree with the notion of requiring applicants to complete time-consuming assignments like this without some kind of compensation, but it’s not an uncommon practice. I would tend to give them the benefit of the doubt on it. If they steal it, it will be a good indication to you that it’s a place where you wouldn’t want to work anyway. And if you really want to, if they do steal it, you can always write a scathing Google review of their company saying what happened.