a good chunk of your resources go to running the GUI
That's not actually true, unless by "resources" you mean "power to run the GPU."
even on Microsoft's Azure cloud service most instances run some kind of Linux
I think that's a misleading statement. That's like saying that, just because Linux has WINE, most Linux installations run some form of Windows. True, you can run Linux as guests on Azure, but the implementation and management is based on Hyper-V and Windows Server.
There are a large number of systems that use all Windows servers, from original EverQuest to Xbox Live to Stack Overflow. It is totally possible to run a distributed, all-Windows server farm, and if you're much more familiar with Windows than with Linux, and people-time is more precious than server-licenses, then that's clearly a possible route.
Personally, I would never do it; each time I've been involved with using Windows for any kind of server for real, it's ended in frustration and a port to Linux. But it is absolutely doable and possibly the right choice for the right team.