How profitable was GPU mining in 2011-12?
Question in title: similar to how profitable it is now.

The numbers he is giving you don't seem unlikely. Using the Bitcoin price of those days he probably could have gotten more Bitcoins than 31 by simply straight up buying them instead of the graphics cards. And if he accurately accounts for the electricity costs it was probably not profitable at all.

His luck (and the reason you are asking this question now) came when the price of Bitcoin went up.


  because he was in a "hard to access" mining pool.


That sounds like a bit of a misunderstanding tbh.