Yes, like Vitamin_C said, players develop just fine at the BL level, probably better there than in the minors because of the higher coaching. The catch is that he must play to develop. If he is going to ride the pine at the BL level then you are better of leaving him down.
As for the specific player, he probably doesn't have a ton of growth left. He will pick up 2-4 points per category more than likely. I'm not sure where you are in your season, but you can probably find a much better option on the FA market for cheap. He will OPS under .600, potentially under .550 and his glove will more than likely not develop enough to be even close to a premier defender. Feel free to give him a shot, but I personally don't think that he is a big leaguer at all. Someone else can feel free to disagree with me.
As far as "rushing" players to big leagues, this doesn't really exist in terms of development. If a guy plays everyday, he will develop. Some people like to hold guys back to delay starting their arb clock (i'm not a big fan of this), but developmentally players are fine being called up young.
12/8/2018 2:54 PM (edited)