Besides that, if England remains allied to France, it would probably lead to a French domination of the continent. I am not saying that Britain stoped France OTL, but British support was crucial in stopping France )as was the Dutch, Spanish, Austrian, Prussian etc). A French dominated Europe can not be advantages to England, certainly considering that it is likely that France remains strong in both India and Northern America.He would need to prove his non-catholic credentials and would have to promise to raise his children as Protestants (as Charles II did for his eldest daughters).
If he did that then he would probably keep his throne. It would however sink the British as it was William III who introduced the Bank of England etc. that enabled the British to win their empire (ironically sometimes at the cost to the Dutch).
Had James continued then Britain's finances would have been in a similar state to the French and we all know were that leads!
James losing his throne was more about his lack of judgement and a monarchical temperament which was more suited to a hundred years previously than it was about his Catholicism per se. He was a popular king at his accession, and he squandered an awful lot of goodwill in a remarkably short time by his maladroit political skills. He might have even kept it had he been just prepared to fight for it, instead of suffering some sort of breakdown and then fleeing after the invasion.
And frankly, even had James somehow managed to keep enough of the army together to beat William as he had Monmouth, there would have been some other rebellion before long. Too many of England's powerful had been alienated. The same is true, therefore, even if William meets with an untimely death - these Protestant grandees would find some other way to put Anne or Mary on the throne.