your idea of Reginald Pole is odd as Reginald Pole was a Cardinal at the time, and isn't the oldest of the Poles, his brother Henry Pole, 1st Baron Montagu is 8 years older and his mother Margaret Pole is alive and well in 1536 (they were all killed in 1539-1541 in OTL) any way the Poles never wanted the Crown in OTL, and were killed because Reginald Pole was the leading opponent of Henry's divorce from Catherine of Aragon, that linked with Henry's paranoia that every one and their mother was after his Crown, a paranoia few in his government shared
Actually, it seems that even if Reginald was a member of the clergy (he only became Cardinal in December 1536) apparently he was really considered by the Imperial Ambassador in England, Eustace Chapuys, as a possible husband to Mary before. I found this reference here, even if only in footnotes:
http://www.british-history.ac.uk/report.aspx?compid=87964
It's from a collection of State Papers of Spain in 1536. In the footnote 2 I've found this reference:
"After that Chapuys was consulted, and asked whether he (Pole) was as highly connected in England as reported,
and whether he would or would not make a fit husband for princess Mary. Chapuys' affirmative answer, dated the 8th of November, but referring to a preceding report of his "more than a year ago," is published at full in part i., p. 323."
However, the most interesting of these letters is that they show who Charles V wanted as the husband of Mary. Here, from the letter of June 20th 1536 from the Emperor to Don Diego De Mendoça and Chapuys:
"Whereas the Emperor's wish has always been to preserve the old friendship, alliances, treaties, confederations, and good understanding between himself and his very dear and much beloved brother, Henry king of England and France, lord of Ireland, &c., whereas he is now more desirous than ever of removing any obstacles that may stand in the way of the confirmation of the said friendship and alliance, and of rendering it closer and more binding, as well as indissoluble,
by means of a marriage between our cousin the Princess Mary and his brother-in-law, the Infante of Portugal, Dom Luiz, he appoints his faithful and beloved councillors D. Diego de Mendoza and Messire Eustace Chapuys, Doctor-es-droits, to whom he gives full powers to treat about the said alliance and marriage."
From June 21st 1536, instructions to Don Diego de Mendoça:
"
Is to bring about a marriage between Dom Luiz, Infante of Portugal, and princess Mary of England.—Asti, 21 June 1536."
And here from the letter of the Emperor to Chapuys in June 30th:
"
With regard to the marriage of the Infante of Portugal [Dom Luiz] and our cousin, the Princess (Mary), We should be extremely glad if it could be brought about. It would be a very suitable match for both parties, besides which, it might possibly be the means of bringing back the King to the obedience of the Church.
True, if the marriage is to be made, it would be required that in the marriage settlements, if not before, the Princess should be declared legitimate heiress to the English throne in case of the King dying without male children;—a thing which, considering the manifestations lately made by the King himself, and the words which Cromwell has let out to you, appears to Us not unlikely."
So, it seems that in 1536 Charles V wanted Mary married to the brother of John III of Portugal, Luís, Duke of Beja and Prior of the Order of Saint John of Jerusalem. Interesting enough, IOTL Luís had only one bastard son, Anthony, who in 1580 was the defeated claimant to the throne of Portugal against Philip II. If ITTL he marries Mary as Charles V wished, the future king of England might have a claim to the kingdom of Portugal if the main line of the Aviz still go extinct. We could have an Anglo-Portuguese union ITTL.