Matt Kemp and Clayton Kershaw became the 4th and 5th players drafted by Logan White to be voted on or selected as an NL All-Star.  The only NL team to sign and develop as many as 4 players is the Brewers and while Fielder, Weeks and Braun are great players, note that lowest player picked in that group was Fielder at 7th overall in 2002 (Weeks was 2nd overall in 2003 and Braun was 5th overall in 2005).  The Brewers other signed and developed player since 2002 was Gallardo.

The Red Sox also have had 5 All-Star players who were signed and developed since 2002, Jon Lester, Jonathan Papelbon, Dustin Pedroia, Clay Buchholz and Jacoby Ellsbury.

The Diamondbacks and Rockies have drafted and developed one All-Star player apiece since 2002, Justin Upton (2005, first overall) and Troy Tulowitzki (2005, 7th overall pick). 

The Padres have not signed and developed an All-Star player since Jake Peavy (15th Round pick in 1999).  The Giants have 3 players, Matt Cain, 2002, First Round, 25th overall, Brian Wilson, 2003, 24th round and Tim Lincecum 2006, First Round 10th overall.

BTW, the 2005 first round has had 6 All-Stars (all position players, 5 college) and that doesn't include Andrew McCutchen (who is trying to be the first Pirate player drafted and developed as an All-Star in 2000s and Ricky Romero.

Finally, All-Star game selections are subjective and in some cases (though not with the Dodgers over the past several years) requirement to pick one player from each team skews this kind of review.