Not necessarily. I was flying from EWR to ATL last week, and had a chance to observe the loading process through my window. The priority bags were being loaded to one side of the hold, while all others were either in another hold, or off to the other side.

As a result, my bag was actually out first ... On both this flight, and my return, priority tags worked perfectly with CO (unlike AF where the agent at check-in actually told me that the ground staff at CDG totally ignore the tags).

Cheers,

GenevaFlyer