From my own experience, it does, at least when it's something that nobody could have done anything about (like a death) But it, takes more time than we usually think it will or should. Again, just from my own experience, we at first may have to not think about whatever it is, but then over time we kind of start to pull out of the "mental file" marked "process later" some of the parts of whatever happened; and over a period of time we process each part until the whole thing just doesn't have a whole lot of emotion attached to it. That's not saying that, for example, in the case of someone who has passed away, we don't still miss them at times, or in some ways; but it's so much less and feels so much smaller.
How it has always felt to me is as if everything surrounding the event is what we process, think about until we make peace with it, and eventually we make some kind of peace with whatever it is.
If it's a death that has recently happened we don't just tell ourselves to be numb, and we don't just feel numb. Things go on that actually do numb us soon after the death, and gradually the numbness starts to wear off.
I have no doubt that there are some very extreme and awful losses/events that people don't ever get over (in fact they're so unimaginable for most people I can't even make myself put into words an example here. Under most circumstances, though (and even with some horrible things and overwhelming losses) we actually do get over it.
One problem can be, though, that when you've been through something but it's old enough that it has lost its emotional punch for you, if it's big enough it will still be a part of your life; and it may be as much a part of your life/history as, say, the color of your hair or the school you went to. So it has no emotional impact for you. But, others who have't had a similar experience can be very uncomfortable about it if you mention it. In fact they can think you "haven't moved on" when, in fact, you've moved on - but you don't have amnesia. Also, in the case of losing someone, sometimes they were so much a part of your life that not mentioning them means you have to leave big gaps in your "story" any time you're talking about a time in your life when they were here.
With "wounds" that have been inflicted by someone (whether intentionally or not), I think it can be trickier because the person who knows he has been victimized by someone else can have a need to have the other person (or at least someone) acknowledge what happened and that it was wrong. There can be a need for some form of justice as well. Sometimes a person may be able to put it past him and do whatever processing has to be done (and this part can be similar to other types of hurts, like death) if he gets a simple acknowledgement and/or apology. So, while I can't speak for everyone, I can say that what makes some "wounds" not heal is that the process can't be complete without those additional elements (like the acknowledgement and apology). Making things right again would be another thing the person may wish he could have happen (at least ideally), but even that could be "gotten over" better with the other elements.
Photo: ME Whelan