No it wouldn't. Hitting one missile with another missile is literally like trying to shoot a bullet with another bullet.
The other thing is...there are nuclear weapons that send up a single pod in the atmosphere, then open up with multiple projectiles to overwhelm any defense systems. There are also cruise missiles that can be launched via submarines and cruise under radar.
Long story short, there is no way to stop a nuclear attack from a country like Russia. That's actually a key part of the stability...no one being immune to getting hit...and both sides being able to fukk you up severely with a response if you do strike first.