The situation is not quite the same for chainsaw mills, as you only clamp a guide onto the bar which doesn't hold the saw rigid, although it will probably have some effect on the frequency and amplitude of the vibrations. The chains on mills are also sharpened differently to cross cutting chains and this may have an influence on the amplitude of vibrations.
We have not had a problem with the chainsaw mill but that is an approved fitment whereas the log cutting device we used was not approved by the chainsaw manufacturer. We have heard of another person who had broken damper springs on their chainsaw after using it for a long period clamped to a log cutting device.
Chainsaws powered by single cylinder recipricating engines will always produce vibrations but in modern saws these vibrations are isolated from the operator or damped to a safe level in normal use. The Control of Vibration at Work Regs 2005 give a good insight into the subject.
This post comes from my other half, who is interested in this topic.