Yes, 2001 was a really rough year for Edward and Sophie.The Fake Sheikh episode occurred in the spring of 2001, and then the accusations about Edward's production company "stalking" William came in late summer, I think (whenever the academic year at St. Andrew's began.) Sophie suffered the ectopic pregnancy in December 2001. It must've been a hugely difficult time for them because, due to the scandals relating to their respective businesses, I think Edward and Sophie knew they would have to give up their jobs, and I suspect that they spent much of 2001 trying to wrap up their business commitments (which I think was a hard enough thing to do, since they had both founded their own companies and were, of course, very committed to them). Clearly they were trying to start a family, too, but by early 2002 they had announced that they were stepping down from their careers to be full-time royals, and their baby plans had suffered a serious setback (and they faced the possibility that they might not be able to have children at all).
I remember all the headlines and scandals that Edward and Sophie were dealing with at that time, but it's when I look at things in hindsight that I think the same thing you do: the fact that their relationship withstood all of that is really incredible. It makes it especially nice to see that, all these years later, Edward and Sophie seem to be quite a happy pair, and they have a lovely family. I suspect those difficult early years must have brought the two of them even closer together. I agree with Mermaid1962 that a longer courtship certainly seems to benefit royal couples. Edward and Sophie certainly seemed to have a solid relationship before they married, and I'm sure the fact that they really knew and understood each other made it easier for them to get through the tough stuff together.