By my count there are about 60 men (and one woman) who are members of the Hall of Fame but never played major league baseball.
This includes about 30 or so players from the N-e-g-r-o leagues who never got the chance top play in the bigs, it includes 7 umpires (out of 8) about 20 or so executives, and at least 3 managers (McCarthy, Selee, Weaver).
For those who have mentioned broadcasters, there is not a single broadcaster who is a Hall of Fame inductee. The Hall does present the Ford Frick Award to broadcasters, as well as the J.G Taylor Spink Award for writers, but the winners of these awards, while being recognized within the walls of the HOF, are not actual inductees.
And a good catch by Connor - Connie Mack did indeed play in the National League before 1900. (He was a catcher - not a good one, but he did play)