@Martin: There is current a bug listed in the vagrant-azure repository (https://github.com/MSOpenTech/vagrant-azure/issues/29) which is asking to use a precaptured image in Azure. This might be different from what you're asking, but it would be good to add an issue to see if it is something that would be considered by the MS Open Tech team.
Windows Azure Web Sites adds a web.config to your deployment which wires up iisnode to look for server.js. Your express package was saying that your application start file was app.js
another way to fix this would be to modify the web.config to point to app.js, this way if server.js was still required for your application to run iisnode would use app.js as your application entry point and server.js could still be referenced from your code.