Example of Flex/AIR - Greg's Toolkit
My boss sent me this yesterday and I think it's one of the coolest examples of Flex/AIR I've seen in a while. Greg's Toolkit (I love the product, don't love the name so much) is a desktop/mobile application that let's you monitor your Amazon web service assets. It gives you a real time view of your instances. I don't have any great screen shots, but I'll steal one from his site:

His application essentially turns your Amazon assets into a virtual server room, allowing you to work with them in a much simpler, quicker fashion then heading over to Amazon's web site.
Greg's Toolkit is available for desktop, iOS, and soon for Android tablets.
By the way, if any of my readers are building cool AIR applications, drop me a line.

So first all - it is VERY easy to call a ColdFusion server from an AIR desktop app or an AIR-based mobile app. It's also easy via a native or PhoneGap app too. Basically, it's easy to use CF from your apps.
To be clear though, we are talking about one CF server. So your N desktop apps would call one CF server. We aren't talking about running CF "inside" the app itself. I figure you know that, but it seems to trip up some people.
To your specific question about CFPDF. CFPDF is used to manipulate PDFs. One feature is extracting text. So you could build an AIR app that - on the desktop - prompts the user to select a PDF from their system. It could then send the bits to CF, CF does it's thing and returns the text, and then the app renders the text.
Make sense?
Is that even possible or will this bring my CFPDF dreams to an abrupt close?