I just have no idea if it will work on OpenVZ, I know from a few threads that I have read there are some issues with openVZ and desktops. Not totally sure if that is this case as well.
If you wouldn't mind throwing me a VPS for a bit I'll gladly give it a shot.
I'm actually coming to you live from a containerized desktop (Xvnc) environment at this very moment, Ubu 14.04 w/ MATE, 1920x1080 res, even added some goodies along the way, FF, Skype, TBird, Filezilla, Nmap, GIMP, just to see what I could get away with. I'll admit I have concerns about security so I won't be leaving it unattended for long periods or hang out in WHMCS with it any time soon, but as
nunim indicated, these are indeed possible.
Kubuntu/Ubuntu Desktop was stable for a while but has been crap latesly
CentOS 5/6 tested spendidly with Gnome 3 or KDE
A stock Debian 7 container with a full Gnome3 + core
Stock Ubuntu 12 & 14 + Gnome seems OK. 13x was pitiful
Fedora just pisses me off due to the assumption of full virtualization which created problems after about 5 minutes. The one time it functioned, the system monitor identified itself as a KVM, among other things it screwed up.
This is the environment I'm on now, which I built a few days back.
http://oohwee.jetfire.support/mate-ubu14-gvfs.png
Not bad for no 3D acceleration - and this is one of the use cases where a cushion of vswap comes in extremely handy.
Okay, enough storytime for my first day. Back to work. It's been a pleasure