Using Visual Studio 11 is it possible to build WinRT applications on Windows 7?
No; WinRT is only available on Windows 8 and AFAIK there have been no announcements that they will be made available in Win7. At BUILD, they specifically said that WinRT was only to be supported on Win8. By extension, you won't be able to develop against WinRT on a Win7 machine because the support just won't be made available.