The high school greats would certainly be a greater advantage than most. I mean Lebron was 27 at the end of last year. He clearly would have made it into the HOF at that point after just winning the title and finals MVP to go along with his 3 regular season MVP awards (as well as all of the All NBA teams, all star appearances, etc.).
Duncan would have been in easily as well. He had 2 regular season MVP's and 2 championships (in which he was the finals mvp in both) before he was 28.
Shaq would have been in. The year he turned 27 he won his first title (as finals mvp) and was the MVP of the league that year. To go along with all of the obscene stats, he gets in.
Kobe gets in with the 3 titles and all of the All NBA, all star games, 2 scoring titles, etc. I mean he was still just 27 in 05-06 and had been in the league 9 years.
Garnett probably gets in though is much closer. The year he was 27 he won the MVP and the Wolves advanced to the WCF. Along with his stats, that probably gets him in.
Dwight Howard is an interesting case. I think all of the off court stuff may keep him out (as well as no titles), but he probably would otherwise deserve to be there as he is a 3 time defensive player of the year, led the league in rebounding 6 times (including 5 straight and 2 other 2nd places), led a very weak Orlando team to the finals, and has more than enough 1st team All NBA awards.
Wade is also interesting. As he only had 6 seasons before he turned 28, but he had the title, won the Finals MVP, had just won the scoring title, and had a number of post-season awards (but no MVP) as well as insane stats overall.
That probably covers the players drafted in the 90's or later. Durant is just 24 so he will probably do enough to get there, but the same could have also been said about Rose and look what happened to him (he is still just 23 so he might actually be able to get there as well), so you just don't know.