I think at this time period any European country would have military adventurism and religious zeal if given the chance. The English were certainly very happy participating in the crusades in the preceding centuries, and in their Protestant conquest of Ireland in the following period. As for concentration of power, I think both England and Spain at the time had very strong monarchies, even if neither of them quite got to the levels of absolutism seen in later centuries. (Although American gold would certainly help them get there.)
Spain was a very specific case. They had literally just reformed their Church, removing many abuses and creating a sort of religious revival. The capture of Granada and expulsion of the Jews also had a profound impact on religious life in Spain. There was also the issue that Spain had a very large military force after the capitulation of Granada. This basically created a class of bored, landless noble men, eager to seek out their fortune and do God's duty against heretics and infidels. North Africa was a popular idea as a destination of continuing the Reconquista, but the discovery of the America's created an even better place to go.
So no, you can't really compare the two. Yes, there would be some adventurism and maybe a little religious zeal, but you can't really compare the two situations if England discovered the Americas, versus Spain. The English Church was still unreformed and in some aspects was very corrupt; it had a stable landholding class, and in many cases the Tudor Dynasty was the beginning of the Enclosure Movement. There is no class of bored knights eager to do God's duty abroad. Sure, you could argue the English were active in the Crusades; that was also three hundred years before. The French, and the Germans were as well. Yet whenever the Papacy desired to Crusade against the Ottomans in the Fifteenth Century, both France, Burgundy and England were seemingly ignorant of these calls.
I also don't think you could say the conquest of Ireland was a
Protestant one. Henry VIII started the reconquest merely as a desire to centralize his authority on the island. The rebellions might've taken on a religious tinge under Elizabeth, as they desired the ability to practice their faith. But that was merely an extension of wishing to be left alone by an encroaching state.
England was a very strong monarchy; Henry VII came to power after the defeat of Richard III and severely restricted the power of the nobility, banning the private armies, ect. But the fact is, Spain was almost demographically suited to conquer the Americas even if the discovery came as a fluke. She had the excess population, a class willing to go forth into the unknown. England's population at this point isn't as large, nor does she have the class that was created in Spain through uniquely Spanish circumstances through the Reconquista. I'm not saying England won't exploit the discovery, as they will... but it'll be exploited in a different way.
I'm still not buying the Gold leads to a Absolute Monarchy. Could you see a weakened Parliament, perhaps through a Monarchy that utilizes the Star Chamber as an arm of royal power? Certainly. But English Absolutism would be very unique from Continental Absolutism. For one thing, the late Stuarts were always desirous of religious liberty, whilst continental Absolutism, such as under Louis XIV, demanded obedience to the state through a single religion. So it's possible that even if the English government has Absolutist Tendencies, it could still have liberties that make it different from a Enlightened Despotism, for example.