Yes, but it is not a replacement for Windows Explorer (not the browser, but the
shell). It runs on top of the Windows desktop, but does not replace it. There
arereplacements to the Windows shell (explorer.exe), such as Aston, but none is
as good as any of the Linux desktops. It is the goal of KDE 4 to run on Windows,
but I have not heard anything about this in a long time. The idea was to make a
common experience available to users, independent of the platform.

Cygwin enables Linux applications to run on Windows, but it isn't a shell per
se. I have used Cygwin and it is good, but you still have to use the Windows
interface to get into Cygwin.