Is it possible to deploy one GAE application from another GAE application?
Is it possible? Yes. The protocol appcfg uses to update apps is entirely HTTP-based, so there's absolutely no reason you couldn't write an app that's capable of deploying other apps (or redeploying itself - self-modifying code)! You may even be able to reuse large parts of appcfg.py to do it.
Is it easy? Probably not. It's quite likely you'll need to understand a decent chunk of appcfg's internals, and the RPCs it uses to upload new apps - not a trivial undertaking. You'll also need to store your credentials in the app, in all likelihood - though you can use a role account that is and admin only for the apps it's deploying to minimize risk there.
In order to redeploy a GAE application, I currently have to install the GAE deployment tools on the system that I am using for deployment. While this process is relatively straight forward, the deployment process is a manual process that does not work from behind a firewall and the deployment tools must be installed on every machine that will be used for updating GAE apps. A more ideal solution would be if I could update a GAE application from another GAE application that I have deployed previously. This would remove the need to have multiple systems configured to deploy apps. 
Since the GAE deployment tools are written in Python and the GAE App Engine supports Python, is it possible to modify appcfg.py to work from within GAE? The use case would be to pull a project from GitHub or some other online repository and update one GAE application from another GAE app. If this is not possible, what is the limiting constraint?