In my son's first year at Princeton, the catcher was all-Ivy and drafted. His back-up (a freshman like my son) was the son of an Assistant GM (now a manager). He started virtually every game the following 3 years and signed after graduating. The next catcher was the son of a famous governor who worked himself into the starting catcher his senior year; and I mean this kid worked, and worked, and worked. I believe the next one was a walk-on - that rare bird the coach never stops talking about (seemingly making the obvious exception seem like the rule).
(The Princeton HC is a former MLB catcher; the only way he doesn't have a catcher who is recruited is if he really really missed on a guy who accepted elsewhere.)
A word on most IVY teams: because rosters aren't maxed out (each team has roughly 28 recruited [Likely Letter] players), every year will bring a couple of players who would be thought of as recruited walkons (i.e., got through admissions on their own). My observation at Princeton is that these walkons are amazingly smart, get their chances in the early part of every season, are treated the exact same as the recruited players by the coach and the team, and generally don't see much playing time past the start of every season - because most were not quite as good as the recruits.
And, consistent with what others have observed about catchers (and other position players): you hit, you play. Princeton catchers all could hit; none could throw out anyone, call a game (catchers at P call their own game), frame pitches, or block breaking balls (tough if the "magic pitch" is, e.g., a back foot slider).
Catchers are the most important position on the field; every blocked ball with a runner on third is equal to an RBI, every runner thrown out is equal to a base hit. You'd think coaches would recognize that. Alas. . . . . .