Does adding a Web Service to my ASP.NET MVC project break the whole concept of MVC?
That Web Service (WCF) depends on the Model layer from my MVC project to communicate with the back-end (so it looks to me like it needs to be part of the MVC solution).
Should I add this to the Controller or Model layer?
It sounds like you should split out your model into its own assembly and reference it from your MVC-application and WCF-application.
If you want to do WebServices MVC-style maybe you should use MVC to build your own REST-application.