It certainly seemed possible that after the failure of Wyatt's Rebellion, Elizabeth would share the fate of Lady Jane Grey:
"For a few weeks...it looked as though the chief result of the rising would be the execution of Elizabeth. Some of the conspirators had certainly hoped to see a marriage between Elizabeth and Courtenay, and to exclude the possibility of a foreign king by placing this English couple on the throne instead of Mary. No sooner had Wyatt's troops dispersed than Elizabeth was summoned to London. Before long, she was transferred from Whitehall to the Tower, where she was subjected to a series of intensive interrogations. Renard [the Spanish ambassador] and [Bishop] Gardiner [Mary's Lord Chancellor] both urged Mary to execute her sister. Elizabeth had been highly circumspect, however, when the plotters had tried to make contact with her, and for all the suspicion and circumstantial evidence, nothing could be pinned on her. It was left to Wyatt himself to undo the damage. Consigned to the scaffold on 11 April, when the government had squeezed all it could out of him, he used his last moments to exculpate Elizabeth. The political difficulty of shedding royal blood in the teeth of such notorious and authoritative testimony to Elizabeth's innocence was evident. Even if Wyatt was lying - and he may have been - scaffold testimonies such as his, uttered when men and women expected imminently to face their creator, were popularly credited with almost gospel truth..." Richard Rex, *The Tudors*, p. 141
https://books.google.com/books?id=oEchnmfzL4MC&pg=PT366
https://books.google.com/books?id=oEchnmfzL4MC&pg=PT367
"During the spring of 1554, both Renard and Charles V pushed hard to have Elizabeth and Courtenay executed as traitors before Philip arrived that summer for his wedding to Mary. But sworn evidence against Elizabeth was lacking: If Wyatt had implicated Elizabeth under torture, as seems likely, he publicly repudiated his confession on the scaffold. In the end, no written evidence against Elizabeth could be produced. Although Lord Russel testified that Wyatt had sent her letters informing her of his plans, she had been careful not to respond. Moreover, the French letters implicating Elizabeth were in cipher, which meant that various interpretations were possible. Then the originals of the letters disappeared from Lord Chancellor Gardiner's possession, quite probably because, as Renard claimed, they implicated Courtenay as well as Elizabeth, and Gardiner wished, above all, to shield Courtenay.
"The result was that Mary found herself in the awkward position of having to explain to her Spanish supporters why her enemies were not subject to capital punishment. As she told Renard, 'Courtenay was certainly accused by several other prisoners of having had a share in the plot.' He had communicated with Peter Carew, who had 'arranged a marriage between him and Elizabeth' by means of a 'cipher, carved on a guitar.' Even given these circumstances, Mary explained, 'the law as laid down by the English parliament did not inflict the capital penalty on those who had consented to treason if they had committed no overt act.'
"When even less evidence was found against Elizabeth, she was released to Woodstock under close house arrest..." Susan Frye, *Elizabeth I: The Competition for Representation* (Oxford UP 1996), p. 73
http://books.google.com/books?id=dNjE5Xs2UnoC&pg=PA73
Suppose that Wyatt implicates Elizabeth in order to save his own life? (If he implicated her at all, even temporarily, in OTL, it was apparently only to say that she acknowledged one of his letters--urging her to get as far away from London as possible--with a verbal message of thanks. He was led to believe that if he would implicate her more deeply, his own life might be spared, but this bait was evidently insufficient in OTL.
http://books.google.com/books?id=MViElWWfijsC&pg=PA123 My POD is that it does suffice.) Mary is convinced by Renard that the kingdom will know no peace as long as her sister lives, for Elizabeth--whether with her consent or not--will be the banner of every anti-Marian, anti-Papist, anti-Spanish movement. So Elizabeth is tried and executed. Consequences?
To answer that question, we should consider why Elizabeth was in much less danger in connection with the so-called "Dudley Conspiracy" of 1555-6--even though the evidence against her there, though far from conclusive, was actually stronger than it was with respect to complicity in Wyatt's Rebellion:
"Like the earlier Wyatt's rebellion, the 1556 plot aimed to put Elizabeth on the throne, but it foundered before any armed rising occurred. When the government started sniffing out suspects, they alighted on members of Elizabeth's household, and arrested five servants including Francis Verney, Kat Ashley, and Giovanni Batista Castiglione. Verney was so deeply implicated in the plot that he was put on trial and found guilty of treason (though pardoned), while Ashley and Castiglione denied complicity but were sent briefly to the Tower and removed permanently from their mistress's household. Anti-Catholic books and seditious papers had been discovered in a cabinet said to belong to Ashley, while Castiglione had already been under suspicion for disseminating subversive literature in London.
"Very likely Elizabeth was not as ignorant about the activities of her household servants as she was to claim, and her protestations of innocence no doubt seemed hollow to Mary. Nonetheless, she was not arrested nor even placed under an armed guard..." Susan Doran, *Queen Elizabeth I* (NYU Press 2003), p. 47
http://books.google.com/books?id=2qX3h_KSs-8C&pg=PA47
Why this much milder treatment compared to 1554, when as David Starkey writes (*Elizabeth: The Struggle for the Throne*, p. 191):
"...the leaders [of the Dudley conspiracy] talked of Elizabeth more freely and with apparently fuller knowledge [than those of the Wyatt rebellion]. And the involvement of her household servants was more extensive and better documented. There is of course nothing which directly implicates her. But the circumstantial evidence for Elizabeth's complicity is much stronger than in 1554..."
http://books.google.com/books?id=7ZGr8tqO-mcC&pg=PA191
One reason may be that the Dudley conspiracy never matured into an actual armed revolt, but as Susan Doran notes in *Queen Elizabeth I* there is another reason:
"In mid-1556 [after Mary's notorious false pregnancy of 1555--DT] few people believed that the queen would produce an heir, and consequently both her English councillors and Spanish husband wanted Elizabeth kept alive and at liberty to prevent a later disputed succession that might well end in a civil war or a French invasion to put Mary Stewart on the throne."
http://books.google.com/books?id=2qX3h_KSs-8C&pg=PA48
As we now know, it was probably already inevitable in 1554 that Mary would not produce an heir, certainly not with Philip. So suppose Elizabeth is executed then, and Mary dies on schedule a few years later. Do we get a disputed succession ending "in a civil war or a French invasion to put Mary Stewart on the throne"?