Henry won't legitimize Fitzroy prior to the Great Matter or he would have just done that historically. Anne was the catalyst only for the Great Matter's timing; without her Henry would have needed more time to push him to the extreme of divorce but he would almost certainly have come to that point anyway if Katherine didn't die first.
The most likely time is, as I already noted, when he puts Mary and Elizabeth back in the succession, without actually legitimizing them. In fact, technically, as Eric Ives argues in his Lady Jane Grey: A Tudor Mystery, Henry's succession plans upended the usual understanding of succession, both by putting in legal bastards and skipping his elder sister's line. Edward's "Deuise" (Device for the Succession) came closer to righting it by skipping his sisters but "normal" succession was not truly renewed until James VI/I succeeded Elizabeth.
By this point, Henry had clearly come to the conclusion that his blood mattered more than his daughters' legitimacy. With such a mindset, he'd definitely consider Fitzroy as worthy of succeeding. Now, does it work? That depends. If Fitzroy is father to a healthy family by now, that ups his chances against barren Mary - depending on age gap his heir could marry Elizabeth and shore up the claims. It is likely Mary needs to be locked up at least, but actually her success stunned everyone - including her cousin the Emperor, who was prepared only to seek her safety when Edward died, not her throne. Mary's successful rebellion (which is what it technically was) was due as much to the fumbles of Northumberland and the rest of Edward's/Jane's government. Seize Mary before she gets to her stronghold, she never has a chance to fight.