I decided to do the exercise for myself. I went back to Detroit's 1st Cup of the run. Note that these numbers would probably be even more so if not for some scouting issues back in the day: for example, Fedorov was considered one of if not the most talented player in his draft class, but the Russian factor impacted his draft position and thus he's not a top pick.
So here are the teams who won the Cup ever since we did in 97 and if they had a player drafted in the Top 5 as one of their core/best 3-5 players:
Year: Where core player was drafted
16: 1st overall, 2nd, 5th (Crosby, Malkin, Kessel)
15: 1st, 3rd (Kane, Toews)
14: 2nd (Doughty)
13: 1st, 3rd (Kane, Toews)
12: 2nd (Doughty)
11: None
10: 1st, 3rd (Kane, Toews)
09: 1st, 2nd (Crosby, Malkin)
08: None
07: 2nd, 3rd (Pronger, Niedermayer)
06: 2nd (Staal)
04: 1st (Lecavalier)
03: 3rd, 5th (Niedermayer, Stevens)
02: 2nd, 4th (Shanahan, Yzerman)
01: None
00: 3rd, 5th (Niedermayer, Stevens)
99: 1st (Modano)
98: 2nd, 4th (Shanahan, Yzerman)
97: 2nd, 4th (Shanahan, Yzerman)
So going back 19 years, only 3 years did a team win where they didn't have a Top 5 pick as one of their core/best players.
Boston won in 2011 over Vancouver (Sedins; 2nd and 3rd overall). Boston won in large part because of a historic goaltending performance by Thomas.
Detroit won in 2008 over Pittsburgh (Crosby, Malkin; 1st and 2nd overall) thanks to the Lidstrom/Datsyuk/Zetterberg core which we were blessed with, but should never expect to happen again from a drafting standpoint.
And Colorado won in 2001 over NJ (Niedermayer, Stevens; 3rd and 5th overall) without a Top 5 pick as a top player.
Seems pretty obvious to me that many elite players come from the top of the draft. They can be added via FA/trade, such as Pronger/Niedermayer with Anaheim, Kessel with Pittsburgh, and Shanahan with Detroit, but Detroit isn't landing elite FA anymore (even if we had room) and is Holland going to make an impact trade? Laugh out loud.