Carpet padding is not a good acoustic absorber, though it is better than nothing at all. For less money and less material used fiberglass, mineral wool, cotton batting, and open-cell foam are vastly superior.
For example: (doing some research turned this up)
You can use a 1" thick piece of Owens Corning 703 compress fiberglass has an NRC absorption coefficient of 0.70 (absorbing 70% of the sound). Thick carpet has an NRC of 0.25 and thick carpet with heavy padding designed to be acoustically effective (the more expensive type) has an NRC of 0.50. The fiberglass is significantly more effective.
I cannot find verifiable NRC data on carpet padding alone, and with hundreds of different types out there it would be hard to find any accurate data on what you are asking about anyway. However, several "experts" in acoustics claim the NRC for thick carpet padding layered to be 1" thick is around 0.30. If accurate, then OC703 is 233% more effective when used in the same thickness.
As such, I don't believe I would waste any time trying to treat specific problems in a room with carpet padding. You are much better served with foam (Auralex, Sonex, and others), OC703 (Auralex ProPanels, RPG, GIK, others), or Mineral Wool (though messy and less rugged).