not more effective, and not for battlefield applications. but a knife is nowhere near as effective as a firearm for a battlefield. so I would say that while a stick and a firearm are for different things, a knife and a firearm are for basically the same thing, and one is a hell of a lot less effective than the other.
basically, there are two reasons for using a knife
1. to kill silently - and, frankly, a silenced firearm is much better for that.
2. if your firearm malfunctions. so, what is better training - to teach a soldier to fix any malfuction quickly, or to teach them to fight with a knife? for that matter, a small backup firearm can weigh almost as little as a knife.
realistically - you need to have a situation where you are stuck with a malfuntioning weapon, you are facing an enemy with a malfunctioning weapon and there is nobody to help either of you, for knife fighting training to pay off. you throw into that that you and the other guy are wearing a chunk of body armor, and have 3 foot metal clubs in your hands (your malfunctioning rifles) and how much good will a knife realy do?