I keep seeing people wanting to do this (or something very similar) and then being surprised at how much it might cost them if they went with Windows Azure. Time for a Q&A.
Short answer: No, definitely not. Madness, sheer madness. (Hopefully that was clear enough)
No because It would cost you a heck of a lot more than just about any other approach to running a blog. A site that can easily be run on a shared hosting solution (as many blogs do today) does not require the rich capabilities of Windows Azure. Capabilities such as simplified deployed and management, dedicated resources, elastic resources, “unlimited” storage etc. It is simply not the type of application the Windows Azure Platform has been designed for.