Patrick, Columba, and Aiden would have done something Henry didn't, which is put himself under his patriarch, which in this case is the Pope.
Also, the power of God is not dependent on any king; it is first dependent upon the Holy Spirit who does work through any of his faithful ministers....of which there were many in Henry VIII's day.
The only bishop who was truly faithful to God, and not to man was one named John Fisher.
Columba intentionally chose NOT to put himself under the Pope. It's a fact. That's why Augustine came to visit. Columba refused the request. Aiden & Patrick were also out of the Celtic Church.