Recently playing with Azure July CTP I stumbled upon an issue which appeared to be known.
The thing that might drive you crazy is that the Publishing wizard does not apply settings from App.Config file. So basically your deployed worker process will have no idea about configuration settings.
It seemed to be a known issue and there are some discussions over here:
other thread: http://social.msdn.microsoft.com/Forums/en-US/windowsazure/thread/604384f0-9d20-4be6-a02c-24ba1ff1bf82
The solution is trivial:
You have to add an environment variable to your user account:
And you need to restart Visual Studio for the change to take place.