I think its certain that Henry would have carried on playing the field whether Jane lived or not - as Heraklia says, it was taken for granted that kings would have their mistresses as well as wives and all parties were expected to know their place. I suppose the real question should be, would Henry have kept Jane as wife if she had lived, or would she too have eventually fallen from favour on some pretext or other?

She had given him a son and had she lived might have been expected to provide more. She seems to have been of a meek and conservative enough disposition not to trouble him, and would probably have dutifully ignored any mistresses, but would this have been enough to ensure she lasted the course?

Henry seems to have genuinely mourned her (not remarrying for several years, calling her his favourite wife, ordering that he should be buried next to her when he died etc), but who can say if this fond regard wasn't only because Jane had fulfilled his queen's most important duty of providing him with a son.