From watching this video, the air pump makes a noise when you start your car as it sends warm air to the catalytic converter. Assuming it's seized you wouldn't hear the noise at startup. Maybe you can feel the pump working too. Looks like disconnecting the wire harness isn't an easy thing if it's similar to this MB SLK55 AMG
2 BIG differences on the SRT6 from this video :
1. there is no separate relay, the air pump relay is in the RCM.
2. The air pump itself is mounted on the driver's side fender well, really easy to get to'
( on the NA models, the pump IS mounted on front of the engine, but there is only one bolt to remove and it comes right out. )