I would think that that particular marriage was doomed anyway; Henry would have probably married another woman, maybe Anne's sister who has already proven fertile, or perhaps Jane Seymour moves up a place and becomes Henry's second queen.
Didn't Anne insist on marriage before her and Henry began their relationship? Perhaps Jane Seymour or some other woman would've been more content being Henry's mistress.
Assuming Catherine dies around the period she did OTL, Henry could just remarry (whether it's a foreign or domestic bride is another question)
Also, assuming Henry did still break with Rome (much more unlikely IMO), I doubt England would've ended up Protestant. The Boleyns were in favor of the Reformation, but without Anne I see the conservatives remaining in power (Wolsey, Moore) and with Mary's eventual accession (assuming Henry continues to have child bearing problems with other women) England returning to the Church.