bdp24,
Yes, I do think it is possible to overdo damping. Specifically with tonearms, I have experimented with the damping fluid level in my Basis Vector arm and heard the difference with the fluid level in the damping trough of an SME arm. Too much damping results in a lifeless sound.
I think tuning of resonance and damping of vibrations in all parts of the reproduction chain is NOT a matter of trying to minimize vibration to the utmost. I was in attendance when a representative from Symposium tried different shelves under a CD player. The very top model that Symposium offered, that does the most to dissipate vibrations as heat, actually sounded quite bad--dry and thin. The representative agreed with this assessment; there can be too much damping.
I've heard the same with devices for placing under speakers, exotic racks, etc. I spoke with someone in the high end industry that has heard hundreds of different systems. He said that he has NEVER liked the sound of a system employing exotic and extremely expensive vibration damping rack/shelves.