I think if it's obvious that one team is trying to advance the ball by hitting or kicking it forward, they can call an illegal forward bat penalty. But even if it's an accident, if the fumbling team recovers or it goes out of bounds (not recovered by either team so it stays with the fumbling team), they will mark it at the spot of the fumble rather than the spot of the recovery or out of bounds. Not sure what the procedure is if the other team recovers after the fumbling team bats it forward (accidentally or otherwise).
I think most players, if they are on the offense during a fumble, will try to either fall on it or push it towards the sideline to prevent a turnover. Much less risky than trying to bat it forward (illegally) and hoping one of your other guys gets it before someone on the other team does.