Yes, it's on the side of the fantastical, but then it's a what-if that assumes Charles won. Charles' objective was the removal of Peter from the throne of Russia in favour of some non-entity that wouldn't bother him. We can say the OP what-if is wholly unrealistic, but the question it posed was what if Sweden wins?Peter being deposed is not going to happen , under any circumstances
even if the Swedes occupy Moscow , the poles and French had been there and it did them no good
there was no worthwhile rival claimant
Peter would still have his Semenovsky and Preobrazhensky elite regiments ( or what's left of them )
they were fanatic in their obedience and his best support
The OP assumes Sweden wins. If Peter is un-deposable, him just ending up dead is a functional alternative. It just might take a bit longer since it involves working out that deposition, like as was done with August the Strong, is not an option.