Without being root, is it possible to download a newer version of KDE and use that as your window manager for a RealVNC server?
It's absolutely possible. If you can
If you can't
That change will allow you to install your build to your home directory, under
Without root access (be it directly or via sudo(1)), installing something as invasive as a full desktop environment (including matching applets, plugins and whatnot) is probably impossible, and at best very ill advised.
What exactly is the objective of this? If it is just access to a newer KDE, updating the distribution is probably simpler and much less risky.