It is possible to host a Juicebox gallery on Google App Engine.
Here is a test gallery I uploaded earlier: http://juiceboxgallery.appspot.com/
I followed the instructions here: http://www.labnol.org/internet/host-web … ine/18801/
The only variation to these instructions was to make sure I had XML files specified in the list of accepted file extensions in the 'app.yaml' file.

No. I used Python v2.7.3 and Google App Engine SDK for Python v1.6.6 (Windows).
The contents of my 'app.yaml' file were as follows:

application: juiceboxgallery 
version: 1
runtime: python
api_version: 1

handlers:
- url: /(.*\.(gif|png|jpeg|jpg|js|css|xml))
  static_files: \1
  upload: (.*\.(gif|png|jpeg|jpg|js|css|xml))

- url: .*
  script: main.py

The 'main.py' file remained unchanged from the 'website.zip' file referenced in the link I posted.

Also, make sure that you are using the latest version of Juicebox (v1.0.2) to ensure that bugs present in earlier versions (which have since been fixed) are not contributing to your problem.
Please see the Upgrading Juicebox section of the Juicebox support pages for details if necessary.

If you continue to experience difficulties, please post the URL to your gallery so that I can take a look.

It looks like incorrect MIME types on your web server might be the cause of your problem.
If you view my test gallery's XML file in a browser, you can see the code itself: http://juiceboxgallery.appspot.com/config.xml
If you view your gallery's XML file in a browser, the browser tries to render the page as if it were HTML: http://www.abbybedford.com/photography/config.xml
Also, If you view the first image in my test gallery directly in a browser, you can see the image: http://juiceboxgallery.appspot.com/images/wide.jpeg
If you view the first image in your gallery directly in a browser, the browser displays the source of the image: http://www.abbybedford.com/photography/images/wide.jpeg
Check with your web host to see if they can help you with this problem.