There are a lot of articles about this topic online. Please read the documentation:
Deploying an Application on Mac OS X [qt-project.org]
Deploying an Application on X11 Platforms [qt-project.org]
Deploying Qt Applications: Linux [qtcentre.org]

If deploy means compile then, theoretically, no. The keyword you are looking for is cross-compiling. However, you still have to test your application once compiled, which will ultimately require a native (possibly virtualized) platform.

Although there are various sites whose authors have hacked OS X to run under VMWare under windows, it does not look like it’s straightforward, never mind the questionable legality.

It’s a different story for Linux – you can run Linux as a VM on Windows using VMware and it works quite well apart from lack of native OpenGL support.

It actually is straightforward, but you are right on the legal note.