Yes, there are separate numbers for each status level (and one for just plain "AAdvantage) for a total of 4.

I haven't phoned the Gold or Platinum number lately, but the Executive number (from what I can tell) is the only one where you have to enter your AAdvantage number before you get routed to the rep. It would be interesting to know what happens if you 'speak' a non-Exec number.