That doesn't always happen — guys like Chris Phillips and Patrik Stefan were first overall picks, so if you tank and that's the year you bottom out...
I know Phillips isn't a franchise player but Patrik Stefan bad? Scanning the draft that year is interesting. Phillips has had one of the best careers of any of the first round picks (Briere would be the other guy) but some others taken that year - with of BoO connections:
56 NY Islanders Zdeno Chara
179 Tampa Bay Pavel Kubina
204 Toronto Tomas Kaberle
239 Ottawa Sami Salo