Not at all. Most NHL talent development is done through an extensive farm system affiliated with and financially supported by their NHL teams, similar in some but not all respects to the MLB.
Prospects pursuing the NCAA route vs junior leagues and the AHL are widely regarded as inferior, facing significantly less stiff competition. A typical player (ie, more than 50% of current players) would grow up advancing through various levels of midget hockey, forgo college to play in one of the CHL leagues (QMJHL, WHL, OHL), from which they would be drafted by an NHL team and assigned to their AHL or ECHL affiliate. This is true even of international players, who are often sent from their home countries to stay with Canadian host families while playing in the Canadian junior leagues.
Making the NHL out of NCAA is the exception, rather than the rule. The system is much, much less subsidized by tax payer funded schooling than the NFL's.