One thing to bring into the discussion here is how important a strong number two center has been, historically, to teams that win the Cup: Beliveau-Richard (8), Clarke-MacLeish (2), Trottier-Goring (4), Gretzky-Messier (4), Lemieux-Francis (2), Yzerman-Fedorov (3), Sakic-Forsberg (2), Crosby-Malkin (3) - that's 30 Cups right there. Now try to imagine each of those teams without the number two guy being on the team, just a big gaping hole filled by the next guy down the depth chart - how many Cups do these teams forfeit without the number two guy? Do the Broad Street Bullies get past the Habs & Bruins without MacLeish? Do the Isles lose their dynasty status if their #2 is Wayne Merrick? Does an aging Trottier slot into #2 spot & get the #1 spot by default when Lemieux is out? Do the contemporary Penguins even sniff a Cup without Malkin? Try to remove the Forsberg piece from the Avalanche puzzle etc. etc. etc.
I'm trying to imagine the Oilers without Messier. Before Sather converted Messier to center, he brought in Kenny Linseman, but when Messier made the successful conversion, he pretty much bumped Linseman from the #2 spot & made him redundant & expendable. So assume with no Messier Sather hangs on to Linseman (so no Krushelnyski) - how do the lines shake out? Sather found that Messier at center had chemistry with Glenn Anderson playing his off-wing on Messier's right side. With no Messier, does Anderson stay on the left side & stick with Gretzky-Kurri? Or does he keep Anderson with Linseman to strengthen the second line? Assuming he does this, for 83 & 84 we might see Anderson-Linseman-Willy Lindstrom as the second unit - but how long beyond this can Jaroslav Pouzar anchor the left of Gretzky-Kurri? Can the Oilers avoid bumping Anderson to the top line, or does Linseman have to rotate through guys like Lindstrom, Pat Hughes, Dave Hunter & later Raimo Summanen & Mark Napier, playing his wings without Anderson? How does a Messier-less Oilers stack up against a Goring-less Isles in the 83 Finals? How many Cups can a Gretzky-Linseman duo pull before Gretzky gets shipped out?
When Goring joined the Islanders, he was touted as "the missing piece of the puzzle." The Isles had been strong playoff performers, but with Goring in the #2 spot behind Trottier, it was widely believed at the time that he was the reason they were able to finally make it over the top.
When Goring joined the Islanders, he was widely touted as being the "missing piece of the puzzle," & the Isles went on to win four Cups with Goring as #2 behind Trottier, with Goring picking up a Smythe recognizing his clutch play. Now, at the time the Isles were probably strong enough to go the distance without him, particularly given the weak competition in 81 & 82, but they may have struggled to hit that same high mark of going 4/5 in the Finals.
But, yeah, 30 Cups with teams having strong number twos. I'd say there is substantial evidence to suggest that historically, having a strong number two center, dramatically increases the chances of the teams winning the Cup.