Another consideration you have to take is when the player becomes a UFA - at 27 years old or 7 seasons. There isn't much point, aside from trade value of his potential, in drafting someone in the first round who may not start for you for a decade.
Here is a quick list of goalies who played in 120 games (arbitrary - two seasons as starter?) between the ages of 18 and 26, between 2000-2001 and this current season.
http://www.hockey-reference.com/play...ed#stats::none
15 of the 32 were drafted in the first round (between 1994 and 2006). In that same period, 36 goalies were taken in the first round. So 15/36 first round picks ended up playing in 120 games before becoming a UFA.
Note that James Reimer needs to play 16 games next season to qualify for 120 before 27. Assuming he does, that makes 33 goalies, and he isn't a first-round pick.
I'm sure there are some flaws in this study, but it was the quickest way I could think of.