What if Mary Tudor had publicly designated Mary Stuart as heir to the throne of England, prior to Mary Tudor's own death?

Mary Tudor had threatened to publicly and formally designate some other heir to the throne of England, instead of Elizabeth Tudor, if Elizabeth didn't publicly swear to an oath of religious tolerance during her reign. Elizabeth was a Protestant, but, unlike her father or her sister, she did not persecute her subjects merely for practicing one religion or another, as long as they did not openly rebel against her reign. The most probable alternative would have been Mary Stuart, briefly Queen of France, and the future Queen of Scotland, and a very staunch Catholic. My suspicion is that such a public declaration of support for Mary Stuart's claim for the throne of England from the dying Mary Tudor might well have provoked a Franco-Scottish invasion in support of her claims, and, that this invasion might well have been successful. If so, a true reign of terror against Protestants in England might have shortly ensued. We have only to look at what Mary Stuart's mother-in-law -- Catherine de Medici -- did in France to see that. The St. Bartholomew Day Massacre is still infamous, but, it was highly effective in suppressing the Protestant Huguenots, and effectively saved France for the Pope. Instead of occasional burnings and torturings of the Spanish Inquisition type, the French tend to favor full scale massacres of the "kill them all, let God sort them out!" type. So, is an extermination campaign against all Protestants, and a permanently Catholic England in the cards, if the future Elizabeth I of England doesn't agree to religious tolerance just before her sister's death?