If you're meaning strictly grown as in drafted by their teams, likely many of the teams in the 70s and 80s were composed of players that were drafted by them. Yes players were traded, but free agency wasn't as big of a deal until the early 90s. Players generally stayed with the team that drafted them.
However, in soccer if I understand the European system, you sign with a club at an extremely young age. Seems to me there are U12 academy teams for some of the European teams. I don't think NHL teams ever groomed players from that age onwards. You may have to go back to the days prior to the formation of the NHL in 1917 to find teams that are all brought up through a certain club. Even then, I'm not entirely sure that you had teams that were like European soccer teams are.
But it can be largely assumed that until the formation of the NHA in 1909, that the majority of teams who challenged for the Stanley Cup were local in nature. Though by local I mean they played where they lived, not were born there. Even the Dawson City Nuggets who challenged the Ottawa Senators for the Stanley Cup in 1905 featured players who were born in the Ottawa area.