Running at all times does not equate to being a server. Nor does being headless. The important point is for it to serve clients. In this case, it could at most tenuously be a server in the sense that it would be listening to have code uploaded to it. That would more be a secondary function for the convenience of getting code onto it though, as that portion would not require being on MacOSX. It's the desktop functions that require MacOSX.

In any event, that's still a far cry from being an enterprise server. Generally, it should serve the needs of the entire enterprise and not just a single department. There should also be full vendor support for the complete solution, and a high level of fault tolerance to really be enterprise.