Yes, it's possible.
Draw some display object to a BitmapData (the stage, for example) and crop it if neccesary (the second param of BitmapData::draw will help you out here).
Then, convert the raw pixel data to JPEG or PNG using some encoder. I'm sure up to this point, this is what those tutorials will explain you how to do.
Now, the third step is different but simple enough. Instead of sending the image data to a server side script, use a FileReference object. Since Flash Player 10, it has a method called save, that prompts the user to save a file locally.
Since this is a desktop app, you could also make it an AIR app. This will give more direct access to the file system and other features, in case you need them.