I’m wary about giving my honest thoughts on this matter because they’re kind of…controversial (like, I’ve gotten a lot of backlash for expressing my views on this before), tbh, so imma just–
First, we don’t actually know with 100% certainty that she rejected that offer (I mean, obviously she rejected at the very least the public title of only mistress, but privately is another matter). That’s kind of just the prevailing idea that’s put forth based on the Vatican letters (but these are probably not the only ones Henry wrote, also we don’t have hers, also we don’t have definite dates for any except the one dated by the remark about the papal legate, and another dated by its remarks about when she contracted the Sweat), based on her leaving for Hever for the summer (which, wasn’t, honestly, unusual? There were usually way fewer courtiers on the court’s summer progress, a lot of them left for their family homes), based on also, imo, the implication that
a) Henry would never have married someone that had ‘put out’ before their marriage
b) He only married her because it was the ‘only way’ to have sex with her. And for literally no other reason.
It’s entirely possible that she was his mistress (which is a pretty broad definition w/ a lot of possibilities attached as well– a mistress in the sense of courtly love? a mistress in the sense of what was allowed within the parameters of a courtship
dans la chambre? variations in between?) before he actually proposed marriage.
And if this did happen, I actually think in any scenario in which he had yet to have a son by K(o)A, he would have eventually proposed, realizing that she was a well-suited choice of a Queen Consort and also that he wanted to spend his life with her. Basically, that he would have had that dawning realization in 1527, or 28, or whatever, that Chapuys spoke so eloquently of in 1530:
…the love of the King for the Lady is so great that he would not give her up for the eldest daughter of France, or anyone else in the world.
In an AU where he gave this offer and K(o)A already had a son?
I do think he would have kept that promise. Because, during the entirety of his betrothal to Anne, he did. I think that was probably a big part of her anger at his affairs during their marriage– that he would be with no one else for at least six years (possibly at least a year of their marriage, too), but take a mistress during her second and third pregnancies (Madge Sheldon, I think it was? The Seymour affair was kept to courtship only) was unconscionable to her. She couldn’t reconcile it to how faithful he had been to her before.
Would he have lost interest eventually? Maybe, it is hard to say with any certainty. It’s often said their relationship was weak, tenuous, and based on no real love, connection, or affection, and that this is so clear because it deteriorated/fell apart ‘so quickly’.
But the thing is, it didn’t fall apart ‘so quickly’. Their marriage was only three years, it’s true, and the last (even before May ‘36) was definitely worse than the first two, but before that they’d had a betrothal that defied the societal expectations for its length (betrothals were long processes if one of the betrothed was a child when it was made– otherwise, there were no ‘long engagements’ with the nobility of years, that simply wasn’t done), from 1527(at the latest)– 1532.
They fought during that period of time, it’s true (this is usually mentioned as evidence that their relationship was always unstable, volatile, ‘only based on sex’). He grumbled once about how she’d spoken harshly to him, that Katherine had never spoken to him that way. Another fight had apparently been so bad that she refused to speak with him, until he was reduced to asking her relatives to intercede with Anne on his behalf, “with tears.”
And he could have thrown the towel in at any point. Could’ve said, “you know what, I’ve had enough of this” at any of the times she spoke sharply to him, and like…still continued to try for an annulment and marry a French royal (Francois was always eager to make an alliance against Charles V, for reasons both personal and political– he’d even offered Henry his sixteen-year-old daughter’s hand in marriage– a day, or mere days, after Anne’s execution), or a number of other alternatives.
But he never did. And in a lot of ways, he would’ve had an easier going with the annulment process if he had, and it would’ve seemed more credible to a lot of people had he made clear that his intentions were to marry another foreign royal once it had been achieved.
He didn’t, because he wanted to marry Anne specifically, and have an heir with Anne, specifically. So, I think he must have loved her just as specifically.
It’s this that makes me believe he wouldn’t have ‘lost interest’ eventually had she accepted the title, in a world/AU without the obstacles he had (lack of a male heir, Charles V and others blockading his attempts to find solutions to this problem, etc.).