ESPN did an analysis of NCAA performance vs regular-season performance, and players who played better in the tournament not only got drafted higher, but also had longer careers than players who didn't. I think it was in their recent analytics issue. Can't find the article online.
Low sample size though, but it looks like it flies right in the wind of what Danny's saying.
I wouldn't be surprised if this is true, but not necessarily for the right reasons.
Interestingly, I believe I read an article about how players who saw their "projected draft spot" get better due to a good tourney tend to be more likely to underperform for their relative draft spot. On the flipside, players who saw their "projected draft spot" get worse due to a bad tournament game tend to out perform their draft slot. The implication of this article was that if you were projected to be a 15-20 pick based on 30 games, then had a great tourney and were picked 6th, you tended to play in the NBA like a 15-20 pick. And vice versa.
Now both of these could be true. It could be true that a good tourney does get you a better draft slot (but it could be undeserved). I also think it's absolutely true that getting drafted higher would lead to a longer career, even if you aren't good. Think about how many bad players are undrafted FAs, play 1 year, then are out. But if you're a first rounder and suck, you usually get at least 4 years because it's almost automatic to pick up those team options. Then, because of "pedigree," other teams keep taking chances. Kandi, Marcus Banks, Gerald Green, Thabeet, Darko, etc, all probably got more chances simply due to rep than comparable undrafted talent.