Can an old Thorens Table be "Over Dampend" to the point where sound is adversely effected?

A lot of people like to dampen these older Thornes tables either on the interior of the wooden plinth or all over the inner metal spring board, and arm board, they use things like "Blue Tac" or that Dynamat stuff in car doors. It will kill the sound and rob the life out of the music.

Despite what some here have been propagating for years....over-damping of turntables, arms etc is not only possible, but can deleteriously affect the sound.

You do have to be careful. But damping a plinth usually dosen't get you in trouble, unless that plinth is so floppy to begin with that all you really did was to change the resonant frequency!

One area where people get in trouble is damping the arm board. The arm board has to be rigidly coupled to the plinth to insure that it moves in whatever plane the plinth moves (a corollary is that if the arm board is of a different material from the plinth it can introduce a coloration all by itself). If you've damped it incorrectly, that may not happen and the result is that the pickup will interpret the difference between the plinth and the base of the arm as a coloration. 

The other problem you have to really be keen on is to make sure that you are not treating the turntable as a sort of tone control to synergize with weaknesses elsewhere in the system.

"Atmasphere"...What is an example of damping correctly?

Using an appropriate damping material (extensional when damping surfaces; constrained when damping between surfaces), not using damping when coupling is required (such as between the arm and the plinth), not using damping materials on the arm in such a way that the performance is compromised. For the most part, common sense.

If your damping is done correctly its impossible to overdo it.