Could probably look at Boston as the real example of building without top picks. They have been a contender forever it seems.
Yeh, they are pretty much the only team post-lockout who have had extended success doing it semi-"old fashioned way"...
but at the same time, especially their first "window" from ~2007-2014 a lot of that success was built through the draft and a combo of skill and luck there.
Bergeron (#45 2003), Krejci (#63 2004), Marchand (#71 2006) and Lucic (#50 2006) were 4 of the 5 most important skaters when they had their first big window. And then Chara was a UFA signing.
Good luck to any team drafting: a HHoF 1C, a league average 1C over prime, a close to HHoF winger and an All-star winger... all with picks after #45, over a 4 year span!
And they also drafted Kessel, Seguin and Hamilton top 10... all of whom turned into great players and they traded for assets that helped too.
Their "current" window of 2017 to present? Started with 3 of those 4 guys still there and still very important. 1 still is...
Annnd added to by, yeh, the draft and hitting on some stars with Pastrnak (#25 2014) and McAvoy (#14 2016)... who are their best fwd and best Dman.