Way back in the dark ages, we called it "Nylon Thump". Even after only sitting for a week or so, nylon-ply tires would rattle teeth for the fitst couple of miles. Some of the other ply material such as rayon, polyester, or Aramid didn't have as much of a problem, but tires that sit for months or years at a time might end up with permanent distortion to the plies. At highway speed, old tires can have catastrophic ply failures with virtually no warning, so if you're planning to do more than just tool around the neighborhood at low speed, better replace them.
Jerry