Yes?
It's called investing in your platform.
MS already makes more than $1 billion a year on Azure, so if they're partnering with the Azure team they definitely have the money to build up the infrastructure, plus they're likely paying for it with Live subscription money as well.
They aren't building it out of the kindness of their heart. They're putting money into their servers so that developers have enough servers to use the platform. The goal is that developers will then use this system to create great games, which in turn sells the platform.
300k servers isn't that much of a stretch. When they install an Azure instance, they essentially have shipping containers that are filled with servers. Each container has 1,800-2,500 servers. This information is from 2010, so it's possible each container could have more servers now. Assuming that each container would have its maximum 2,500 servers, that's only 120 additional containers. If each instance only had the minimum 1,800 servers, that's still only 167 containers.
Neowin has pictures of the inside of these containers:
http://www.neowin.net/news/live/09/11/17/inside-windows-azure-server-container
Considering each container takes 24 hours to install, MS only needs a few months to install these new servers. So again, 300,000 sounds like a lot, but with the way servers are installed in datacenters, it's not that much. I'm sure Azure has way more physical servers than that right now.