That's an interesting idea -- I bet the soil & compost forum would have suggestions.

I personally think it would be better for the environment if you could find a way to get it recycled.

Here's an article with some ideas.
disposing of carpet

Here is a website that might help you find a place to recycle it:
http://www.carpetrecovery.org/

Here is a link that might be useful: carpet recovery

If it is natural fiber you might think about running it through a wood chipper. May bind it up but maybe not. Just an idea.

For cat lovers, I make a nice cat house and climbing house out of scrap lumber and even used some cardboard boxes. The cardboard will need some support from a wood frame. They like it if you leave a few "flap" doors to go in and out as they please. If it is natural fiber I don't see what harm it would do the the enviroment.