Sure.
In the Kustomize menu, select your character and make a new variation (or change an existing one). Under Abilities, press 1 and choose whichever tournament preset you want (these have trophies beside their names).
Now you can dress them in all sorts of gear and use it in ranked.
Choose any variation, it doesn't matter and set it as default. On PS4 that's the touch pad button. It will now use your cosmetics from that on ranked no matter which you variation you play.