No, it doesn't. Time may heal some wounds, but it doesn't heal all wounds. It never heals wounds inflicted by the tongue. Time can't take away the hurt feelings suffered by those who have been slandered or gossiped about behind their backs. Time can't resolve conflicts between people. Time doesn't repent and time doesn't forgive. The advice to just give angry people space and time to get over whatever it is that has angered them is bad advice. Not only will they not get over it, but they will inevitably infect others with their anger and inflict more wounds with their tongues. Even if enough time passes and they seem to have gotten over it, they really haven't. Whatever it was that angered them, if left unresolved, will always be there. And, what of those whose names they have slandered and whose reputations they have damaged along the way? Time can't take that away. If the angry people seem to have gotten over it, but have not sought forgiveness from those they have damaged, nothing is gained. A false peace results, which is always on the edge of erupting into conflict again.
Time does not heal all wounds. The healing balm of forgiveness is the only cure for some wounds. But, that healing balm cannot be applied when those in conflict refuse to talk. Communication is the key. Honesty, love, and the desire to be reconciled are pretty important, too.
What was it our Lord taught us? "If your brother sins against you, give him enough time and space and hopefully he'll get over it"? Um, no. We are to go and show our brother (or sister) his (or her) fault. Not later, but now, before things get more heated and ugly. Time is not our ally in the conflict resolution process, but our enemy. The more time that passes, the harder it will be to confront and deal with the issues that caused the conflict.
I wonder why this is so hard for Christians to understand. Actually, I should rephrase that: I wonder why this is so hard for Christians to practice, for surely all Christians know that the right thing to do when they are upset with a brother or sister is to go and talk things out, seeking reconciliation, which flows from their desire to forgive, love, and be at peace with one another. And yet, having spent almost 20 years in various leadership positions in the church (the last four-plus years as a parish pastor), rare is the occasion when Christians actually practice what our Lord preaches. Far more often, when they become upset with someone or something in the congregation, rather than confronting the matter and seeking after reconciliation, they harden their hearts, find like-minded people with whom they can gripe and complain, and even look for ways to get even or to punish their brothers and sisters (or the congregation, in general). Time doesn't help. Usually, if enough time passes and there has been no attempt at reconciliation, the final act of "showing those people" (or, "that congregation)" from these people who have grown angry for this, that, or the other reason is to leave. "Let's see how they get along without us," they think.
One wonders how such people can pray the Lord's Prayer with a clear conscience. They can't really mean it when they pray, "forgive us our trespasses as we forgive those who trespass against us," can they? They are not willing to forgive. They are not even willing to talk, so how can they be ready to forgive? After all, forgiveness is not something we feel in our hearts, but something we give, by way of announcement, to others, on the basis of the forgiveness we have received from the Lord.
Of course, there is guilt on the other end of this equation as well. Those who recognize that there are angry people in the congregation and refuse to confront those people in love and with the desire to restore them gently have failed to practice what our Lord preached as well. It may be easier to simply ignore those people and let them stew, but the right thing to do is to confront them with the honest desire to try to understand where they're coming from and why they're upset. Sometimes, this is impossible, as the angry people refuse to talk, but it is just as sinful not to try to reach out to these people as it is for these people to refuse to seek reconciliation and allow forgiveness to reign. Mom was right, after all, "Two wrongs do not make a right."
Anyway, the whole point is that time definitely does not heal all wounds. Time can't repent and time can't forgive. Time won't heal conflicts within the church. Only Gospel-motivated faith and love for one another, which shows itself forth in a willingness to seek reconciliation and a desire to forgive can do that.