Well, I haven't done any proper tests, but when you level up a drill, it says "+10% training effect."
If you go to the training screen, click drills, upper right corner next to the unlocked drills counter click the "i." It says "A bigger training effect means more quality points gained when you use that drill in training."
I understand that as players gaining more. I suppose it could means gaining bonuses but the special coach they try to get you to hire is for "a training boost" so it would be logical to call it a "+10% training boost" rather than "training effect" then. Or would it? I don't know. "Training experience points" is what they call the points you need to unlock drills (and this is always the same 1 experience point per 0.75% condition used, regardless of drill level.)
So basically I don't know.
I haven't noticed my bonuses going up faster but who knows.