Noble Silence is a Buddhist term said to derive from the buddha's responses to unanswerable questions. Thich Nhat Hanh writes about the practice of Noble Silence at Plum Village here.
Although Noble Silence can imply being externally or physically quiet in the usual sense of refraining from speech, like the (Catholic, Benedictine) monastic Great Silence of the night hours, it doesn't necessarily have implications about speech.
Noble Silence comes about when a person's being, body mind and soul, is fully integrated, when inner turbulence is brought to harmony by a practice and discipline of peace. When that happens, a person's entire life becomes a yoga of peace; their words and actions follow the flow of grace.
I think it would not follow that they cease to be a source of irritation or antagonism — Jesus, prince of peace, was crucified after all. Evidently he irritated and antagonised somebody. He didn't flow unseen through the world. Where the interests of Mammon held sway, he was a sign of contradiction, as his followers will also inevitably be. Persecution always results from this — though we should be cautious, when we are in the majority and the mainstream, of identifying every instance we don't get our own way as intolerable persecution by the insolent Other.
Silence, solitude, simplicity and slowness are the watchwords of spiritual path. They belong to it and characterise it. They are habits of mind and life, a marinade of our whole being. We practice them until they permeate every aspect of who we are. It takes a whole lifetime.
They are not in truth four things but one, facets of the single jewel of faithful discipline. They are found inside. A person can search for them everywhere and never find them, because they are not externally located — ever. Like the Pearl of Great Price in the parable Jesus told, the merchant, the one who deals and trades in such things, has to sell everything to buy the pearl. That is to say, the seeker comes to a point of refraining from trade with the world and its ten thousand things, finds instead the One — integrates, unifies, concentrates, refrains, harmonises, consolidates. This is Christ's work of reconciliation, the realisation of the pearl of great price, which forms over time in the practice of what is natural, Noble Silence clothing every irritation. Noble Silence irridesces around the grit that arises within our being or enters from outside, to make of it a jewel of patience and peace.
External silence, solitude, simplicity and slowness significantly help the development of Noble Silence. Everywhere you find teachers advising that when Jesus said you must give up everything, basically he meant of course you can own things so long as they don't own you. This is and isn't true.
If you practise accumulation you will develop complication and various sorts of noise; then problems will occur. If Noble Silence and the pearl of great price are what you are seeking, owning little and travelling very light helps your endeavour.
If you practice involvement and socialise a lot, it is in theory possible to preserve Noble Silence inside; but you certainly make it harder for yourself.
If you do everything in a hurry and exclude Ma from your life and try to multi-task, there is no inherent reason why this cannot co-exist with Noble Silence, except that you would have to be a master practitioner first; you couldn't develop a silence of the heart through busyness. Well; I don't think so, anyway.
Have you ever read Herman Hesse's book Siddhartha? It is full of insight and wisdom. In response to the merchant's questions, "What do you have to give now? What have you learned? What can you do?" the central character says, "I can think. I can wait. I can fast."
This is the practice of solitude, silence, simplicity and slowness; infinitely versatile, it maximises life's potential, and to some degree respects the uncarved block that allows the possibility in every situation, even though the unfolding of personality and occupation erode it.