I don't think anybody is capable of giving you a firm answer because nobody has done it. You would probably be the first. In fact, when double-checking the info I had found earlier, some of the searches gave your message in the first 3-4 results. Hi Mom!
Cards which support UHD should support 4k. You can try to use the closed driver benchmarks from Phoronix to guesstimate if your intended usage will be passable (http://www.phoronix.com/scan.php?page=article&item=ubuntu_1404_4kgpus). The R7 250E may have issues running a composited desktop. I would not expect the R9 280X to have issues. Most complaints seem to be from people with older cards, but then again, those reporting success all seem to be using closed drivers. I rated success likely enough that I was considering a Dell P2415Q w/ the Intel HD4600 (and replacing my motherboard) or an R9 290X. Make sure you have an exit strategy, though.
