What is the experience using the Google App Engine (GAE) platform to host a Google Omaha server for serving the updates?
Technically, I think it could be done by using the Blobstore API, but I haven't found anything online...
You can use the Google App Engine to write a server as long as you implement the protocol here :
Google Omaha server protocol V3
You could use the blobstore to serve the update packages but that is not absolutely necessary. The packages themselves does not have to be hosted with the same server, in other words, you can put your exe/msi anywhere on the web and just point to it(Package url in the protocol v3) in the GAE server implementation.
One thing to note though, omaha requires either the server to support either ssl or CUP(client update protocol). GAE provides free ssl, address would be https://yourserverapp.appspot.com/address_of_update_POST_page , there are some restrictions in defining the name, please see GAE FAQ about secure connection.