I think it would partially depend on what branch of Protestant they chose,
Because they'd then be more ideologically aligned with Scotland or England, and probably prefer one to the other,
Would have interesting effects when you get to the British Civil War, If Ireland was on side probably no Cromwellian massacres for one,(depending on whether they join in the Presbyterian Scots Prayer book revolt) and so relations are better
If Ireland decided to side against England in wars with Scottish or Dutch in 15/1600's... well it's always been described as a back-door to invasion so England would definitely have to deal with it somehow, probably leading to the conquering and/or something similar to plantation, or at least an English ruling class being instated with garrison troops to keep order(I'm aware how speculative and vague this is sorry it's late
)
If no major clashes(no worse than those experienced by Scotland) possibly remain a part of Unified Isles and hence fewer of the problems in OTL, although no royal house ties in OTL to help along, could some sort of diplomatic alliance or even more extreme merging into a unified whole occur?