In my experience, extended breathing does aid meditation in that it slows many metabolic processes but from a strictly mental standpoint its not an absolute necessity. That being said, I find that, at least in my early stages of meditation, focus on the breath is helpful. It takes me out of my own thoughts on the future or the past or even on what I'm "trying to do" and instead I'm just breathing. Once I've focused on breathing long enough I can become aware of my thoughts regarding the breathing and then begin to direct my thoughts where I would prefer them to go in my meditation.
In light of that, I generally don't try and focus my mind in meditation except when devoting time to direct my thoughts toward someone or an event. My meditation is more focused on simply experiencing the present moment and through it the Force. My thoughts aren't focused on the Force however as that can just as easily lead to focusing on the mental contruct we have of the Force rather than the Force itself.