Technically, you can. It requires you to go in and manually change profiles every time you switch planes though. It would be nice to have a profile attached to a particular plane. Load Plane X, and Profile X loads with it.
My stick is a generic config for all my planes, but I created a second profile for my X56 throttle. One I use for planes with mixture and / or RPM control, and another without. And I switch based on which plane I’m flying. It’s not ideal, but it works. Hopefully at some point they make it so profiles can be attached to planes.