Considering Kane was in a midst of a 7 game scoring slump so bad he and his dad watched video of himself from previous playoff rounds to remind himself he was still a good player, I'd say no, whatever Kane was doing during the period from mid-way through the DET series to Game 4 of the Kings series was NOT the driving force behind the Blackhawks winning games. (Pssssssst.... it was the reunification of Keith and Seabrook on D that turned that series. Tell your friends.)
Toews and Kane certainly got some shifts in together during the comeback in that series. Not as fixed linemates, mind you, but because Q started double-shifting Toews to get him some time away from the Zetterberg matchup, a change from the usual, where he double-shifts Kane to get more offense out of him late (but as I mentioned earlier, Kane was struggling at this point in 2013, so he wasn't getting much extra time for offense). Toews and Zetterberg would battle it out, Zetterberg would go off, Toews would be right back on. Again, this is why corsica.hockey is so much more useful. Instead of some misleading general aggregate, you get a sense of which lines he actually played on, and which are a collection of a shift here and a shift there, 6 minutes here with this combination, 2 minutes there with another.
And Kane? Or was he just an afterthought on this 11% potency power-play?
You're not going to get much arguement from me that Toews was an absolute MONSTER on this playoff run, and that he gets undo criticism based on an unluck sh%. I've been arguing that for years.
But if you're arguing that the impotent 2013 powerplay, and I include both units in that description, was in any way the difference or even a significant contributor to that cup win, you are absolutely out to lunch. They were bad on the PP. Thankfully, they were gods on the PK.
Ive never argued that Kane & Toews together wasn't a nuclear option as far as generating offense. But it's kind of ludicrous to suggest that a combination that lasts roughly 5 games per playoff run is the key driving force of a cup win.
The bulk of the Blackhawks success has come from their ability to put out Toews on one line to absorb the top matchup, win the goal differential battle, and thereby clear the road for Kane and his line - who almost exclusively see heavy ozone starts against weaker QoC - to strike at the soft underbelly. Combine that with a transition D that can torch other teams, and a bottom 6 that could handle the spill-over top-6 opposition, and you had the basis for their success through the cup years.
There's a reason the Kane+Toews combination is brought out in specific scenarios and doesn't last long. You overload your lineup like that in a playoff series, the other team has time to adapt, you're screwed. You just used your nuclear option, what's next? What's the next stage beyond your doomsday device? Now the opponent has taken your best shot, adapted, and you're well and truly ****ed. Thankfully the Blackhawks have never been foolish enough to try that and have kept them on separate lines where they're most effective.
So basically you want me to drag the minimum TOI down so that we can count a couple minutes together here and one minute together there as if it's consequential. A line works together for more than a minute here or there thanks to a double shift late in a game or to escape a matchup. That's the difference between 'playing them together' and them happening to end up on the ice together thanks to circumstance.