With Azure websites (in preview) deployment of Mvc4 projects is in the matter of seconds (I have been using it for some months). If you fork a hosted service, yes deployment does take time if you use the official way. Afaik, you can also use the accelerator for web roles [1] to reduce this delay considerably [2].
Cheers. Unfortunately while we have a web role we have two worker roles running long-background processes to deal with Exchange streaming subscriptions (this isn't really a website, it's an API). This is more than I found when attempting to search for a solution to a quicker deploy, however.
[1]: http://blogs.msdn.com/b/windowsazure/archive/2011/07/12/now-...
[2]: accelerator is no longer being updated (afaik), chiefly because Azure websites are designed to handle the scenario it was developed for.