Yes, this is the site of the final CoP fight (Mission 8-4).
Once you've completed the fight, you can go back and do it again, but just like any other BC, you need someone else who has not done the fight yet to start it.
You'll be done with the CoP Missions yourself though. You can get your ring, view all the CSs, etc.
The place for promathia is connected here but once you fight promathia, can you fight him again? Also, will you be finished and start all over or can you just continue with ur happy go life? I'm a noob so bare with me.