As discussed on some of the other AA threads, the Orange Premium Tags and indeed any Elite tags you may have on your bag do not affect the priority of your baggage being handled behind the scenes. They're just there to make the pax feel good about themselves and so you can easily spot your bags coming off the belt.

Sometimes random screening by the TSA can hold up bags - and you may find a white/blue TSA note inside your bag if they needed to open it.

The only time I know of where you can expedite your bags is when transiting LHR. If you're on a tight connection the check-in agent puts a 'Tx Short' tag on the bag (where x is the connecting terminal). This means the bags will be put on a container that's unloaded first and re-routed to the correct terminal as soon as possible.

Other parts of the world, like HKG attach an RFiD tag to each bag enabling the baggage system to automatically re-route and prioritise bags based on connecting flight information.

Long gone are the days where the baggage handlers take note of your FF status and/or tags.