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I can't give you a definite yes but I'm going to say that they do or its very little. I do know that the VNC Client seems to sleep most of its network activity when its minimized, I base this on two key behaviors that I've noticed.
the VNC client will not update the screen while its minimized, it will wait until its viewed or explicity asked to refresh to do so.
Many many times the VNC Client will not even know if the server is missing while its minimized, that is if connection has been lost due to network issues or if the services was killed abruptly.
However to find out its easy. Get two computers whatever VNC you want and open a session, on the server... scroll a page a few times over and over. Read the bandwidth used on the client with the free net meter program. Minimize and repeat and see if its the same or less.