As porous as that foam is when it hardens, I don't think you'd get a lot of damping. If you can still buy automobile undercoating in a spray can, you might try spraying that on the inside. Part of its job (on the car) is to damp metal resonance. I've heard of people filling the stand tube with lead shot, too, but it has to be a sturdy stand to stand up to getting shot.
Thanks Mike, I will reconsider my approach. My best stands are Koenig and Meyer, they've served me well but I don't ask much of them. Lead is probably more than they are built to take.
Maybe I can use a dowel to shove chunks of high density foam in there. I've got some of that laying around. The undercoating sounds interesting too.