Yes, it's possible to install Android Studio on Windows Server 2012 but you may encounter issues when using the emulator as well as issues sharing code between developers. I have installed it on Windows 2012 servers but these were not being used to share common code between multiple developers.
For the emulator (e.g Intel HAXM), if you have Hyper-V installed and running you will find that the emulator won't run. What I do on my systems (multi-boot desktops and laptop running VMs) is to run a configuration with Hyper-V disabled on boot for when I'm working on my Android development (and other virtualisation technologies.) For a server, you could do the same thing but would need to assess if you need Hyper-V running all the time. If not, the decision is easier. If you do need Hyper-V running on the server then you'll not be able to run the Intel haxm emulator.
The other problem you will encounter is a shared project location for the developers and ensuring they aren't overwriting each others work. By default, each user will maintain their own project space in their home folder, not a shared folder so you may have issues of version control especially if there is a chance they are working on the same project and copying the code to their own project spaces.
You'll need to work out how you are going to handle source code if they are all working on the same code - more likely this will have to be a procedure for checking who is updating code unless you have a technical solution in place for checking code in and out etc.
If all you are doing is providing a development environment and there are no plans to have your coders working on the same code then you should be fine with the only issues being storage depending on the number of developers, code they are developing etc.