In an answer to this question, a pro coach "justified" his publicity stunt of picking Johnny Manziel (a football player) with the 837th overall pick by saying, "No 837th pick has ever played in a major league game.
There are thirty major league teams, and I've heard of 20th round (and higher) picks making it to the majors (although this is rare). That might be somewhere in the 600's for overall picks, 750th, if someone actually made it from the 30th round?
What is the lowest overall draft pick that actually made it to the majors?