Only because David Robinson suffered a season ending injury during the 6th game of the season. The year before they won 59 and they year before that, 62. They were already contenders before they drafted Duncan, but he put them over the top.
They basically added a once a generation player to a 60-win team. Most teams that win the lottery don't already have one of the top 50 players of all time on their roster. It was a unique combination of circumstances that hasn't been duplicated since.
Since Duncan, the only top 3 draft picks to win an NBA championship for the team that drafted them are LeBron James and Kyrie Irving, and that took LeBron leaving so CLE could get the #1 pick three times during his four year abscence, and then coming back and finally winning a title 9 years after being drafted. Again, an unprecedented set of circumstances.
In fact, of the 60 top 3 picks since Duncan was drafted, only 6 have won an NBA title (LeBron, Kyrie, Pau, Bogut, Adam Morrison and Durant). Pau and Morrison won with the Lakers. Bogut and Durant won with GSW.
So, twenty years, six future champions for three organizations and only one that tanked their way to a title (CLE and they had to tank once to get LeBron and tank for four more years before he came back).
Winning the lottery isn't nearly the panacea many in the pro tank crowd would have you believe. Sucking bad enough to get a top 3 pick is much more likely to be followed by several more years of sucking, followed by your top 3 pick getting fed up and leaving to have a better chance at winning a ring elsewhere.
BNM