From what I saw the Elite training grounds did nothing - positive nor negative. I had no buffs running. I checked the last queued item's completion time and it was 2 days 13 hours. I placed the building. The time was exactly the same. Since the building description said "after placed" I cleared the queue and added all the soldiers again and it is still 2 days 13 hours. So nothing happens at all. Several refreshes were involved just to make sure.
I can't say I'm really surprised.
Edit: Did the normally advice clearing of Flash cache and browser cache and reloaded and no effect.