Q Is it possible to prevent the individual Mac users on our network from changing the desktop background on their Macs?
A Not as far as I am aware on the normal client edition of OS X, even in Yosemite. You could perhaps work out a system implemented using permissions for a non-admin user, but admin users certainly cannot have this locked away, and the next time that Mac needed a system update it would all go awry.
OS X Server Yosemite edition, or Server.app 4.1 as it is more properly known, enables this and many other controls for ‘managed users’, and would be the safest way to go if you wanted to implement this robustly and without causing future problems.
Updated from the original, which was first published in MacUser volume 28 issue 07, 2012.