Not sure on the importing into Flash Professional. I would not recommend it, since it is dependent on the Flex framework. It might work if you take into Flash Builder and merge the RSLs into the swf.
As for the player version, you need version 10 or later.
Just did some testing here, and Flash Professional definitely does not like Catalyst projects. Importing to the stage failed silently (gotta love that), while Import to Library appeared to work - I got a MovieClip in my library. However, the clip is empty. I'd guess it is as Chris said, having to do with the fundamental differences in the Flex framework from the way Flash Pro works.
As this did spark my curiosity, I decided to give loading the Catalyst-created project into a Flash Pro project at runtime using ActionScript. I was able to at least get the Catalyst content to appear through this method, but the effects (in this case, a simply button with a Rotate3D effect applied) was a mess.
So the simple answer is "no".