Well, Karl's attack on Moscow could butterfly Napoleon's disaster of 1812 away by proving that it isn't possible to get Russian Bear in his lair, but little else could be achieved, provided that Peter would not perish. There was very little appetite among Russian elites of the day to co-operate with foreign power to advance their internal political agenda (Times of Troubles taught them that), so I would suspect that TLs based on Swedes exploiting internal Russian turmoil are more wishful thinking than solid ideas. Karl could give Russian armies grief until cows come home, Peter would always have another army to throw at him (BTW, I just love the fact that median of Swedish claim of Russian losses, as posted in WP, exceeds well-documented strength of Russian army pre-battle; did Russian army included undead Zombies too?).
Seriously speaking, it all would depend on Peter's guts. Karl would not be able to defeat him in proper "European" sense of the term, neither is Karl likely to find hordes of Quislings among Russians in 1700. However, I can see Peter making unfavourable peace, especially if he would be trapped (the way he did during Prut disaster).
Peter's death is the most intriguing idea, but butterflies are far too great to speak of in general terms. When did he perished? Who else fell? Did he appoint an official regent for little Alexei (just 10 during 1st Narva)? Who? Peter is one of few figures in world history about whom it might be said that they created the wave as much as they rode it...