So basically, you're running Bitcoin on a VPS and using an HTTPS connection from App Engine to signal it what to do? Why not just host the site on your server?
App Engine gives me:Free bandwidth and data storage (with the option to pay for what I use if I go over a gigabyte)
Built-in, already-configured-and-tweaked tools like memcache and BigTable
An architecture where scaling up is built-in (App Engine will automagically replicate my app and distribute it across Google's worldwide content distribution network if it gets a lot of traffic)
And all of that is administered by Google's sysadmins (who are WAY better at that than I am).
But mostly I did it as an experiment and because it was a technical challenge and because lately I'm an App Engine fanboy. I would've been done a day earlier if I'd run everything on the same server and wrote the front end in PHP+MySQL.