Compiz compositing capability will be replaced by Clutter, which will be integrated into the next generation of Metacity window manager, called Mutter. This means you won't need Compiz. Since Mutter is closely integrated, you cannot replace Mutter with Compiz.

GNOME shell uses compositing and is integrated with Mutter, a compositing window manager for X11. Mutter is the next generation of the Metacity window manager which uses the Clutter toolkit for compositing.

GNOME Shell has received some controversy in the free software community because the planned tight integration with Mutter will mean that users of GNOME Shell will not be able to switch to an alternative window manager without breaking their desktop. In particular, users will no longer be able to use Compiz while GNOME Shell is running.[2]. Discussion between the developers of Compiz and GNOME has failed to resolve the issue. However, it will still be possible for users to run the GNOME desktop environment without GNOME Shell and still use whatever window manager they choose.

http://en.wikipedia.org/wiki/GNOME_Shell

Gnome is quoted as saying "'Because the GNOME Shell project wanted "tighter integration" between the panel and window manager than cooperating with the Compiz project would allow, this could actually be true. This mailing list post has more information.'" that statement was made in response to "I can't use Compiz with GNOME Shell!"

Most likely Compiz will be phased out of Gnome Desktops.

It might be best to see how well Compiz works with KDE, LXDE, IceWM, and XFCE.

Compiz works well with Xfce and KDE however the latest KWin effects have better integration into KDE 4.6 Plasmoids. Compiz-Fusion was meant to be a transitionary package for DEs to use in developing their own native effects.

No

compiz is not supported in gnome-shell , gnome-shell uses mutter instead of compiz