I don’t think so.
Character Animator could output a video you can play in Animate, but the concept of a “puppet” is different in the two products. (There was a feature request to move Animate animations into character animator if you want to vote for it.)
To my knowledge-no. I had an issue early on because I was watching the tutorials for Animate, not realizing it was a different program. LOL!
Good Luck. I personally decided just to use CA.