No. GNOME Classic is built on GTK 2 and GNOME 3 uses GTK 3 which is
incompatible. Ubuntu 11.10 and 12.04 use GNOME 3. Classic is history unless
you use an older version or switch to Debian. However, GNOME 2 distros will
soon find that the apps are no longer being supported or developed. This
was the big reason for dropping Classic and moving to the new version. GTK
2 just was not good enough to keep developers happy.

There are GNOME Classic wannabes such as Mate and Cinnamon which you can
install. They come with Mint, but are available for Ubuntu without needing
to switch.