Hello,
I guess nobody will give you a guarantee and unless someone has already used 12.04, the best answers will be based on "educated guesses" / general experience.
Since Alfresco is purely Java-based, you should have no problem running it on Ubuntu 12.04. Since this version of Ubuntu has been released a while ago, you should also have no problems with the 3rd party tools that accompany Alfresco, like ImageMagick, SWFTools etc., i.e. all potential library incompatibilities that may have been should have been fixed already. I currently only know of a few bugs in 10.04 LTS that have been fixed in 12.04, so my bet is you'd probably be better of on the newer version.
Regards
Axel