To my knowledge it's not possible to get the entire skybox image to rotate, even through the use of shaders. If you want scrolling clouds, then they are added to the sky shader as a cloud layer and given a tcmod scroll value.
Please see the Quake III Arena Shader Manual for more details: http://www.qeradiant.com/manual/Q3AShader_Manual/
However, you can do some interesting things via the portalsky functionality that ydnar added into Q3map2. Essentially you create a hollow cube of equal dimensions, build whatever you like in it, and place a _skybox entity at the center of it. Then texture the sky from the rest of your map with any sky shader you like. Q3map2 will automagicly turn the areas of your map textures with the sky shader into a portal that looks into the skybox you created and also scales it up by quite a lot (8x iirc). You could for example make a load of rotating autosprites to represent stars and have them spin around in your skybox.
Warning: Do NOT put patches inside the skybox unless you are willing to use the -patchmeta bsp switch to force all the patches in your level to become solid geometry.
Please see the Q3map2 Wikibook for more information: http://en.wikibooks.org/wiki/Q3Map2
Hope that helps.