I ran 10 "lotteries", slightly different system, I assigned the teams numbers 1-1000 appropriately. Here's what I got.
1. 76ers
2. Magic
3. Bucks
1. Jazz
2. Magic
3. Lakers
1. Magic
2. Jazz
3. 76ers
1. 76ers
2. Bucks
3. Magic
1. 76ers
2. Magic
3. Bucks
1. Magic
2. Lakers
3. Bucks
1. Magic
2. 76ers
3. Bucks
1. Magic
2. Bucks
3. 76ers
1. Bucks
2. Magic
3. Jazz
1. Bucks
2. Nuggets
3. 76ers
So what does this mean?
It's not so surprising to see a non top 3 make it, in my example the Jazz and Lakers were fairly frequent visitors, and also an appearance by the nuggets.
In terms of teams with the number 1 pick in this example: Magic won it 4 times, followed by 76ers with 3, Bucks with 2, and Jazz with 1. So it did relatively hold to form that the Bucks won 20% of the time, but it skewered towards the top 4.
It was difficult to get a team not in the top 6, the only team I had that did it was the Nuggets. Mostly it was the top 6, but no Celtics, interestingly enough.
Take that as you will.