Either you worded that wrong or it is just wrong period. Without doing any research I can think of 2 QB's right off the top of my head drafted in rounds 2-7 that have won playoff games since 2003. Drew Brees (rnd 2) and Tom Brady (rnd 6).Did you mean to say only 1 QB drafted in round 2-7 since 2003 has won a playoff game?
Brees and Brady were drafted BEFORE 2003
Then your sentence should read: Only 1 (yes 1) QB drafted in rounds 2-7 since 2003 has won a playoff game.