In my experience, yes they can and often have in my past. However, I think this depends a lot on the person who has had the recent breakup and how quickly they are able to heal and bounce back from such ordeals. I can only speak for relationships in which I was the one on the rebound (I don't believe I've ever gotten involved with a guy in that situation), but I've had some very successful, long term relationships which had started shortly after another one ended. In one case, there was even technically a bit of overlap...so I know for a fact that it can work, and anyone who says that something always or never works is making a generalization which can't possibly prove true in every circumstance. I think it mostly depends on the state of mind of the person who's "on the rebound"--the new relationship's chances are highest when that person is most emotionally removed from their last relationship. That is to say, the more lingering attachment there is, the less likely that the new relationship will succeed. However, we should also keep in mind that the vast majority of all romantic relationship eventually end, and relationships that started as what some people might classify a "rebound" (which is not at all a precisely defined term) often end for reasons that have little or nothing to do with how they started. Anyway, like all questions of this nature, I think the answer is specific to each individual situation, because no two relationships (or the set of circumstances in which they originated) are the same. So the only way to find out is to give it a try, and like all relationships, to go into it with your eyes wide open and your past firmly relegated to the past as far as your emotional state of mind is concerned.
Hmmm...I think that would depend on what you are defining as a "rebound" relationship. sometimes after a break up, a person might take up with the next available person that comes along just to try to get over the ex. In rare occassions that may turn into something real and deep, but more often than not, something that starts like that usually burns out fast. But if time is the only element you're worrying about, then that's another matter. And just because you may have some lingering feelings for an ex when you first embark on a new relationship, that doesn't automatically mean it's a rebound relationship and it's doomed. It depends on how much you respect the new person, how much you have in common and how well you get along, and how willing you are to open up again to someone and something new.