It would be difficult. I believe Sigismund favored Catholics in Sweden that caused the majority Protestant populace to become wary of him. Duke Charles was also an intriguer who was probably hoping to dispose Sigismund at some point anyways. If Charles is out of the picture--he dies early (he died in 1611 anyways) would force the Swedish Privy Council to name a new Regent. If such a power vacuum exists, Sigismund might be able to exert some influence over the appointment.
I don't see Sweden becoming a formal part of the Commonwealth, but a personal union between the two countries is possible--but I wonder for how long. Poland was much more expansive and populous than Sweden, it could become possible that the Vasa Kings of Poland use Swedish resources for foreign adventures, or even in Poland to perhaps centralize the country. The Vasa monarchs of Poland and Sweden would have to be very careful; they would not be able to be the devout Catholics they were in OTL and would have to be tolerant of the Protestants.
Most importantly, if the Thirty Years War breaks out, there won't be any Swedish intervention on behalf of the Protestants. If anything, the Vasa monarchies remain neutral. There also won't be any deluge (assuming the personal union lasts that long) which can only be good for Sweden. I can't see the union lasting too long, but definately possible for a short while, assuming calm heads oversee it.