Wayland can run GTK applications when using GTK+ 3.x where there is the Wayland back-end and is in very good shape and GTK+ can handle multiple back-ends. GTK's Wayland support is just a matter of passing --enable-wayland-backend while configuring GTK+ for building.
While Wayland/Weston is part of the Ubuntu archive and there is GTK+ 3.x, Canonical hasn't yet enabled the Wayland back-end. For the Launchpad bug that's tracking the Wayland GTK+ support status for the Ubuntu package, it's now been updated by Iain Lane of Canonical. Unfortunately, it's not a good update.
The Canonical developer has now marked this bug as "won't fix" for Ubuntu. Iain says that "this isn't going to be possible." His reasoning is that they won't want libgtk-3.0 having a dependency on Wayland and libxkbcommon. Unfortunately the GTK back-ends can't be split out of the standard GTK package. Instead Iain just sees using a Personal Package Archive (PPA) for distributing a Wayland-ified GTK.
Oh, I'm sorry but this isn't going to be possible.
Extra backends get compiled right into GDK. This means that libgtk-3-0 gets a dependency on wayland and libxkbcommon and there's no way to split it out. It would always have been difficult to get wayland into main as a build dep of GTK, but it really won't be possible to have GTK+ depending on wayland.
Sorry. I suggest you keep on going with a PPA if folks want to use GTK+3 in Ubuntu with its wayland backend.