VNC will use as much or as little bandwidth as you throw at it. It works by sending an update whenever the client requests it. A client usually sends a request when it's done receiving and displaying the last update. So if the bandwidth is small, then each update will come slower, so you'll have a low framerate.

Of course, it might end up wasting bandwidth if you have a big pipe, as it could potentially update the VNC client more often than the screen gets updated, but in a two-node network with this being the only service, who cares. Okay, it could overload the CPU, but I (or someone else) could update the VNC server to fix that problem.