Whether or not being able to sit still in silence is a "spiritual discipline," I do not know. I have learned by experience, that it is probably one of the most valuable abilities I have spent time practicing, with the deepest and most far-ranging side-effects.
Do you have an "internal dialogue"?
If so, have you noticed how much more difficult it is to listen to the words of an external speaker, that is, your family or friends, at the same time that this internal dialogue is taking place?
Imagine having control over when you think (and what you think about) and when you do not.
You could develop this control, with practice. Simply practicing attending to yourself and to God, in a quiet place, every day.
First, here are two reasons not to do so.
1. There is work to be done. It is good to attain the momentum of doing, of getting things done, and maintain the habit of doing so.
2. Every one who tries to sit still for longer than a few minutes finds their mind wandering and often discovers a great deal of pain hidden within themselves.
On the other hand, the Lord says, "Be still, and know that I am God."
In response to 1., I will point out that when one is "getting things done", one may or may not be getting the right things done. "All is vanity." How much of your day was spent on activities you could look back on at the end of your life and feel proud that you spent your time on? Doing the wrong thing is more damning than anything else, and actually takes more time (given clean up, or the time it takes to undo what's been done) than if one had just started on the correct thing in the first place. Without a careful consideration of what needs to be done, the doing of them may be more bad than it is good. And careful consideration is best done with a quiet mind. So the habit of sitting quietly and attending to oneself and God is the best and, owing to the reduction in detours, the most efficient means of "getting things done."
In response to 2., the difficulty of a thing does not deny the worth of a thing. Indeed, difficulty is a necessary (if insufficient) condition of worthwhile pursuits. The wandering of the mind is exactly the problem and is to be expected. It will decrease with practice. Imagine being able to control when you think (and what you think about). Not just this or that part of your day would be improved, but your day entire. The consciousness you use during the entirety of your day would be clearer, and better, and more effective. Is it not a desirable goal?
For practical guidance on how to begin this discipline today (without having to become a Buddhist), read Herbert Benson's excellent research on the subject and follow his advice. You can learn the simple steps of practicing sitting still at: http://www.ucop.edu/humres/eap/relaxationrespone.html
or follow (the very similar) advice of John Main, at
http://www.wccm-usa.org/meditate.asp
Let me know how it goes.