Can an arm be "too" damped, too non-resonant? Are those two things the same?Not really.
Removing resonance from the arm tube is a good thing and its impossible to overdamp the arm tube in this regard. One **massive** problem with that though: messing with the mechanical resonance caused by the compliance of the cantilever and the cartridge/arm mass is not good, unless by doing so you get it inside the 7-12Hz window. So if you are applying damping materials to the arm, you can mess that up and with dreadful results.
Damping can be done by a damping trough too; which is an entirely different form of damping, but IME that can lead to problems especially if the LP is not perfectly flat. Generally speaking the arm will not need this kind of damping if the mechanical resonance is in the right window.
So you have to be careful when bandying these terms about. They can mean three or four different things depending on who you're talking to and that's on a good day!