Our beer was completely fermented out before we put it in the barrel. I, personally would not want any, or as little as possible, fermentation to occur in the barrel.
Remember, you really can clean this thing between fillings. A rinse is about all it can get.
Now if you plan to use this thing on only one batch, fermenting in the barrel might be interesting, I have no experience with that. We are on our second batch in the barrel.