To buy a Drag Pak car new from dodge you have to "submit a Dodge Challenger Drag Pak Application" and they will decide if you get one. That clearly is not "available from any dealers inventory for sale to the general public". That doesn't mean you cant enter a Drag Pak car in SCTA, it just means you have to enter it as a "2010 Dodge Challenger" and it's production status will be based on how closely it compares to a production Dodge Challenger. For the 2010 car the Drag Pak hood is different so you may have to change it out for a stock shaped hood. I think that's the only real difference that would matter in your case.
But it could get messy for some of the other year vehicles. For the 2011 car, it comes with a V10 which the production Challenger never did, so that may be an engine swap and have to run in GC.
So you could run a Drag Pak car but it may not be considered Production.