I am not certain that I am interpreting your post correctly, but if you have found just the awning material, what you are considering may be possible. The attachment method on the side of the coach for the awning fabric would essentially be identical, and from all appearances the way the fabric attaches to the roller tube on the A & E and Carefree appear to be very similar.
If what you are wanting to do is install an A & E roller tube and awning on your Carefree arms, you are likely headed for trouble as the attaching methodologies are quite different. If the A & E that was on my Overlander is any evidence, the methods for the roller tubes are very different based on compairson with one of my friend's Carefrees on a 1968 Sovereign
I think that if you are considering switching to a complete A & E system, you will likely be disappointed. When I spoke with the A & E representative, I was advised that the awning arms are no longer available for any Airstream products more than 10 years old.
I finally gave up trying to save my old A & E Travel Awn 5,000 - - but not until I had spent nearly 1/2 the price of a new Zip Dee awning. I now have Zip Dees on the curbside as well as window awnings for the bathroom and bedroom.
Good luck in finding a solution to your awning dilemma.