So here is a pic without it built:
Note that the time required says 17 days to complete.
Now after the training grounds are built:
Now the new faster time is... 34 days?
It works fine for my reg barracks but not the elite. I considered that maybe it couldn't handle changing an existing list so I emptied the queue and let the set finish. Then built the training grounds again and refilled the list and the same thing: 34days for the "fast" version. Destroyed the grounds and 17 days for the "slow" version.
Edit: So apparently the problem is the buff (skunk) mixing with the grounds bonus. After the buff expired, I built the grounds again and the 17 days went down to 11 as it should. Then when I placed another Skunk buff the total jumped to 31 days.