Since the Rangers won the cup in 1994, the Detroit Red Wings are the only team since then that didn't have multiple top 10 picks within 6 drafts prior to their 1st cup victory. Detroit built their dynasty thru being ahead of the curve in drafting Russian and Swedish players but even then the dynasty started with #4 overall Yzerman and #3 overall Primeau in 1990 allowed them to acquire Brendan Shanahan in 1997, the year they won their 1st cup in the 90's.
Not all of those picks were actually roster players on the cup champion. Some like Brayden Schenn were used to acquire pieces to put the team over the top but without Doughty at #2 overall, the kings don't win two cups. Same goes with Toews and Kane in Chicago, Scott Neidermayer in New Jersey, Sakic in Colorado. Colorado used Lindros at #1 overall to acquire a ton of talent that helped win a cup. Anaheim packaged two top 10 drafted players to get Pronger. The one team where it was not led by a top 10 picked player was Boston. Boston flubbed on Zach Hamill and traded Kessel before the cup. Seguin did have an impact in the conference finals but was not a real difference maker the rest of the playoffs.
The point of this is that picking in the top 10 multiple times seems to be one of the things shared by modern Stanley Cup winners before they went on their cup run. It makes a ton of sense since you need elite talent to win a cup. The Flyers could get lucky picking late but the odds are better the higher up you are the draft. Unless you think one of the top 10 picks on this team is an elite difference maker, looking at prior cups winners, the odds says that they will need another top 10 pick or two to get a cup.
Again, this is just a lazy analysis. Yeah, Chicago got Toews and Kane in the top five, LA got Doughty, etc. But we have Giroux already, so it's not like we're devoid of elite talent and need the pick to get one. We can still build around Giroux without top ten picks...
As for having "top ten picks" for the sake of having top ten picks, we have Voracek, Schenn, Schenn, Couturier, Lecavalier, and Coburn which I would assume is at or above the average. But this doesn't matter at all (which implies that it doesn't matter how many teams since 1994 have had multiple top ten picks).
The Flyers don't need a lottery ticket. They need a #1 defender. You don't need one to get the other, though I won't deny it helps. I just get frustrated when people suggest that this team is somehow set back if they don't have a top ten pick at the end of the year.