Can We Have Different Wallpapers For Each Workspace under Gnome?

The short answer is not without applying patches.

But you could use a different window manager / desktop environment. Enlightenment, for example, supports this feature.

Answer to a very old question if anyone still wondering: Yes, you can.

Using a Gnome extension called Walkpaper. Install, open its preferences/options, assign wallpaper to each workspace and done.