Elizabeth I barely survived a bout with smallpox in 1562. Based purely on genealogical principles, Mary Stuart would have been her successor. Would the Queen of Scots ever taken the English throne?
There are arguments both ways. Mary was viewed as a politique in 1562, she had a kingdom behind her, there was no single obvious Protestant candidate, and the Council would have been divided. The Mary Tudor precedent would have given her additional hope. On the other hand, unlike Mary Tudor, the Queen of Scots was a foreigner, and the leading English nobles would have been in no mood to repeat their experience with a Catholic Queen. They probably would have reached an agreement on a male Protestant candidate fairly quickly.
In the end, it probably would have come down to Mary’s willingness to provide guarantees that would have satisfied the Protestants. It would have been an unstable situation at best, and in the long run, as in Protestant Scotland, it could not have worked.