Flash Catalyst does support inserting SWF content. In addition, these swfs can be controlled in a limited fashion by Flash Catalyst. What you described is totally achievable with Flash Catalyst.
I am completely new to flash catalyst, and I am slowly learning, but I can't seem to get my swf file to reliably play and pause. Maybe you could walk me through this..
This is what I've done..
1st - I imported my swf movie
2nd - I made a button and added an interaction (On click, Play Action Sequence)
3rd - In the timeline I selected the action sequence I just made for my button and then selected my swf movie on the stage.
4th - Back in the timeline I clicked 'add action' > swf control > play - play()
5th - at the same point on the timeline I also added 'add action' > swf control > stop - stop()
When I tested my scene, It would start it then, stop it, but I couldn't click on it again to start it. What do I need to do to be able to click my play/pause button and start and stop the movie whenever I want?