Do we need to pursue times of silence for our spiritual health?
Absolutely. Jesus, even though there weren't any stereos and televisions in his day, still took his disciples aside and said, "Come away a little while and rest." The crowds provided the pressure in those days, and he set an example for us.
Psalm 46 likewise says, "Be still and know that I am God." Even when you are doing Christian stuff, being busy can rob you of the very walk and communion with God that provides the kind of depth that, in the busyness, people are looking to you for.
Christians are the only people on the planet who, as they walk into frenzied situations, should have about them an aroma of Christ, a steadiness, and a strength that doesn't look nervous, frenzied, or overly fretful. People ought to detect that, though everyone else is nervous and running around, the Christian in the room seems to have roots sunk down into something solid. The wind is blowing, but the Christian isn't on the verge of uprooting.
It is really important that we keep our roots sunk deep and our branches spread high in the glory of God so that there is a peace and a steadiness about us as Christians.