No he has not. It's pointless to look at turnover stat only, you need to look at it in in conjunction with dribble stats, as most turnover are results of failed dribble attempts. So in PL Kagawa has a 0.6 dribbles per game (only 10 dribbles completed in 18(4) matches) with a losses of the ball at 1.1 and he is dispossessed 1.8 times a game. Adnan has 1.9 dribbles completed per match (51 in 27(12) games), while he looses the ball 2 times per match and is dispossessed 2.1. So the difference in losses and successful dribbles is much better for Januzaj. It's kind of 46 dribble suc rate. He just attempts them more. While Kagawa is by far likely to loose the ball than dribble past an opponent, his suc rate is like 20%, two times worse. Dribbling is not the only thing that leads to these looses, but it does account for the most of them.
Overall, Kagawa looses the ball by mistakes and tackles at 2.9 times a match, and he manages 0.9 chances created, 0.6 dribbles, 0.8 shots per game and gets 0.4 times fouled. Yes, shots and chances created are not directly linked with the looses of the ball, but they do show that how many time a player find himself in dangerous situations, how many times he actually threatens opposition. And a player is more likely to loose a ball near the opponent's box, than in the middle of the park, when opponents rarely press you as hard.
So i would say that Kagawa dispossession stats are actually very bad. It's just impossible to see how exactly he manages to loose so many ball. He does not dribble, he is not really active in the opposition half in terms of being involved in shots or creating of ones. Of course we watch the games and see that Kagawa is very bad with protecting the ball, every time there is a physical challenge coming in he is likely to loose the ball. He does not loose it much because his energy levels are good and he manages to run a lot, find open spaces, mostly away from dangerous areas. And he also passes it short before opponent will go near him to actually make a tackle. So in a way Kagawa is simply not really involved in tackles by opposition and in 50-50s. Which is hardly a good thing for a AM. I definitely prefer someone with real skill, that maybe will loose the ball much more, but will actually threaten like Adnan. The gets fouled 2.2 times a game, he manages 1.7 shots, 1.9 dribbles and creates 1.1 chances for partners. You can just see this guy is at the center of things, he makes them happening.