Right, so Henry VIII's relationship with MB lasted 1522 to 1525, when he took up with her sister. The last pregnancy of Catherine of Aragon was 1518, so it was pretty obvious from about 1521 that she wasn't going to have any more children.
If we take into account that AB only got to be Queen because she refused to have sex with HVIII before marriage (probably a cynical move in response to his cavalier treatment of MB) then MB has to basically do the same thing to become Queen. OTL Henry didn't try to divorce CofA until 1527 and it took 6 years to do it by fair means or foul.
Now, the main problem is the Papacy. Until his death in September 1523 there was Adrian VI, who had been given a scholarship by one of Richard III's sisters and was the tutor of Charles V. The next guy is more promising: Clement VII sent a legate to England to get help against Charles V in the Italian Wars and then allied with Francois 1er late in 1524. If HVIII had promised support sometime before Oct 1524 (when he wasn't needed due to F1er's presence) in return for an annulment he might have got one. What is certain is that he can't wait until the Sack of Rome in 1527. Can anyone make out the effects on the Italian Wars that Henry's involvement would have?
The question is, can MB string HVIII along for 2 years? If so, they can still only have a maximum of one child before Henry gets bored of her in 1525 (OTL Henry Carey, 1st Baron Hunsdon, who would be the Elizabeth I analogue). Still, if the child was a son, the relationship might survive a few more years: Henry might not even feel it necessary to further secure the succession until her death (OTL 1543), leaving "Henry IX" as an unquestionably legitimate son in his early twenties at his father's death. The effects of this would be immense!