No, fedora Mate has no flatpaks by default. I do use them on my machine though. They are not as integrated to the system as snaps on Ubuntu but they update only when I tell them to and I like the additional security benefits of the flatpak project overall.
I think security wise it got worse. With traditional package repos someone still does some due diligence. Also it's not clear what's going on, and that is a huge prerequisite for security.
I use free software to own my computer, if it decides on its own when to update like snaps do that defeats the purpose.