The supply situation could be stabilized with help from Mazepa, but not the manpower issue. I think that the Swedes might get away with offering Status Quo Ante--Pyotr will use it as a chance to rebuild, face the Ottomans, and remove Karl's Polish puppet--but ~15 yrs down the line the next GNW will pretty much doom Sweden unless they can by some miracle secure a European alliance (Austria?) and the Russo-Swedish wars become yet another theater of the Wars of the Austrian Succession, 7YW, etc. If somehow they can ally both Britain for subsidies (France, Sweden's traditional subsidizer, is losing its economic power by this point) and Austria to deflect Russian land ambitions they could hang on for quite a while...I'd imagine that Pyotr or his successors eventually get the site of St. Petersburg but Sweden keeps Estonia&Livonia and possibly is "compensated" with land in Karelia.
But IMO the only real victory for Sweden in the GNW is an invasion of Russia immediately after Narva preferably with the Tsar in Swedish custody or buried in Swedish soil as I discussed earlier. If this did happen Sweden would have to either become much more colonial than IOTL (I could see them allying with the British and inheriting much of the French Empire--or vice versa) or would have to massively industrialize early on and maintain a technological and economic advantage over the Russians (Is it fantasy to think that Ferguson-style breach-loaders might make their way into the elite units of the Swedish Army?). The most interesting timeline IMO is one where they renew their traditional French alliance following the reorganization of powers after the WotAS (mostly to oppose Prussia, now their main Baltic rival), and the combined French and Swedish fleets take naval supremacy from the British. Ultimately Sweden is given some of Britain's colonies after the TTL 7YW, incl. Prince Rupert's land, Newfoundland, some Indian trade ports, and some Caribbean islands. IDK where the 13 colonies end up; they're far too populated and far too British for them to become Swedish or French. Maybe a weird alternate universe where the British support the United States against the tyrannical French and their bloodthirsty Swedish mercenaries?