A lot of nobles defected to William, but they didn't take so many troops with them (admittedly, a lot of the rank and file just went home). But even if James had kept his army together , it wouldn't have stood much chance against William's Dutch veterans. James "army" was the Squire , and his tenant farmers and the farm lad, armed with left over Civil War weapons. William's army was professional soldiers.
How would a contest between Henry and James, no William involved , have gone. Say the letter of invitation was sent to Henry not William ? Hard to say. Both would have had the same standard of troops. James would have had an advantage, since he would have more artillery, and the fairly well trained (but small) guards regiments.
But would Henry have gone into rebellion ? It's hard to say, because he died so young, we don't really know much about his personality. But he seems to me, for the little it's worth, to have been a pretty honourable sort of man, more like Charles II than James. I don't think he would have rebelled. Opposed James in Parliament maybe (which could have led to a spiraling crisis). And, if Henry stayed by James side in 1688, (as I think he would have, so long as James had not turned on him) a lot of those nobles would have stayed. Henry would have been a guarantee , so to speak.
These were not Tudor times but they could be brutal enough. Remember, even Marlborough ended up in the Tower at one point. And Algernon Sydney, the Duke of Monmouth, Lord Russell were executed as slickly as any of the Tudors could have wished. Though, "in the Tower" need not mean execution. Just being kept out the way could have been effective.
It is important to realise that William did not care a fig about England. His reason for invading, and for remaining, was that he wanted English resources to fight France. The war with France was critical to the Netherlands. It wasn't critical to England. As long as James was king, England would at best be neutral, might even ally with France.
The only sure way for William to get English resources (mainly money) was to rule the country. To do that he had to be King. If he wasn't king it wasn't worth it to him. I'm sure , though, that he would have gone home with his ships heavy with loot, and probably a good Treaty as well. Leaving the Whigs who had invited him over to James's vengeance. They knew that, if William abandoned them , they were worse than dead men. And William would play the game only as long as it was worth while to him.
Actually, thinking about it, I think the most likely scenario would be that William would not invade. The discontented would invite him , as OTL, but the presence of Henry would be the deciding factor that would make William decline. OTL he was very dubious and uncertain about it, and nearly refused. Add a Henry, and I don't think he would take the chance. The fact that he was the only possible Protestant "savior" was his trump card. Remove that, I don't think there would have been a Glorious Revolution. Perhaps (probably) some sort of revolution/rebellion/civil war, but not a Glorious Revolution. Perhaps something more like the Wars of the Roses. Though all Charles I's children seemed fond of one another, there did not seem much sibling rivalry.