Finally managed to get pesta running under Windows Azure. It wasn't too difficult actually. The July CTP of Windows Azure SDK supported MVC projects as a web role out of the box. No hacking necessary.
However, when I first got it running, pesta did not seem to inject the javascript libraries and gadgets were not rendered properly. It turns out that when deploying the MVC project, the CloudService does not include files with BuildAction set as JavascriptContent. This needs to be changed to Content so that the files will be deployed along with the project.
You can see the server running at http://pesta.cloudapp.net/.
The next part will not be so straightforward; getting pesta's persistent storage to use Windows Azure storage. Well, I hope I'm wrong.