Polish Vasas

Wladislaw IV of Poland requested permission from the Pope to marry an unspecified Protestant princess. There was talk of him marrying Elisabeth 'la Grecque' of the Palatine (sister of the future Princess Rakoczi and Electress Sophie). But the Catholic aristocracy of Poland was against it, and apparently the Pope too. Not to mention Elisabeth was not interested in the Catholic king, and they say Wladislaw lost interest after he discovered it would not convince the Swedes to elect him as their king.

What if (and a rather sizeable if at that) the Pope had granted the dispensation, the nobility had begrudgingly accepted the new queen, and the new queen had been forced/disposed to marry Wladislaw, would it have granted a new lease of life to the Polish Vasas? or were their days already numbered?
 
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