The very first thread I tried to post to on this site, I suggested (in response to a challenge that the USA somehow acquire a bit of European territory, apparently to draw us into the Great War from the get-go) that the USA somehow wind up annexing Ireland. I came up with a half-baked (I guess) scenario where the British decide they have to wash their hands of the troublesome island but are afraid to let it go loose and certainly don't want some European continental power to get influence over it, so they turn to President Teddy Roosevelt...I swear I was brand new to the site and had no idea what a cliche the almighty TR was around here--I just figured he was a bold figure and one the British just might trust to accept Ireland into the Union (or as a Commonwealth a la Puerto Rico) on terms the UK (less Ireland now) could live with. And that membership in the Union, on superstate or commonwealth terms, with our secular Constitution, could defuse and moderate sectarian religious conflict--the Catholics would be masters by their majority, but the Protestants (who after all dominated higher society) would have sufficient backing from the overwhelmingly Protestant US elitedom--but then again the Catholics would have advocates, from many Catholic US citizens--including of course a whole raft of Irish-Americans.
I thought it was kind of neat, I wasn't prepared for the criticism--and for having my thunder stolen because I had to wait a long time to be approved for site membership. I honestly still think it's kind of neat.
But ASB as we say of course--Britain was hardly that ready that soon to pack it in in favor of the Yankee new kid on the block, no matter how far the preliminaries of the "special relationship" may have advanced by that point. Nor would Ireland satisfy the intentions of the OP, being off to the west of the war and all that, never mind that it was spectacularly more the Heligoland or the other favored contenders. And I don't know that the Irish would have been as thrilled as I imagined.
Ok--the point here is, just because there are a heck of a lot of Irish-Americans, and quite a lot of them back then around the first decade of th 20th century fresh over from the Auld Sod, didn't give the USA much of a claim to Ireland, any more than all the 1848 refugee Germans gave us claims to German territory, or the fact that today Los Angeles is the second-largest city in numbers of Korean or Iranian inhabitants (after Seoul and Teheran respectively) lets us annex either South Korea or Iran.
Lots of Icelanders, even conceivably more of them than lived in Iceland, does not give Canada a claim on Iceland. Before 1900 anyway, I suppose it wouldn't be Canada but the UK that might cash in such a claim if it were honored. But no one then or now would honor it. If the Icelanders in Canada felt so passionate about it as to organize a filibuster and go back and stage a revolution against the Danish crown, and then having fought off the Danish authorities came to Ottawa petitioning for their new Republic (or principality or whatever) to join Canada--well maybe then it might work that way. I still think that in the pre-WWI context London would intervene, and like as not mediate the return of Iceland to the Danish allegiance, or perhaps their independence.
I still think the obvious route is to figure on 18th century dynastic wars and trophies of war; the weak link is still figuring why Britain might value Iceland as an asset worth taking from the Danish crown (as opposed to other concessions they might prefer). Also considering that Iceland taken is one less hostage the British could use to hold the Danish kingdom to ransom to bring them to heel, whereas Iceland under nominal Danish control is not only such a potential hostage but also subject to British influence via British control of the high seas and its huge merchant fleet--I guess I can see why the British didn't actually do this OTL. And I may have a confused impression of the general tenor of Anglo-Danish relations in the 18th century colored by how bad they got during the Napoleonic Wars.
But that's still the angle to approach it from, I'm convinced.
To be sure--if Iceland were somehow added, in a "fit of absent-mindedness" or by virtue of some cunning plan, to the list of British possessions in the 18th or early 19th century, I suppose that the later crises in Iceland that might all the more easily lead to a major Icelandic exodus to Canada might help explain why Iceland gets roped into the Canadian federation rather than remaining under the British crown as a separate dominion in its own right or set free completely.
Again it's hard for me to imagine Iceland going to Canada without figuring Greenland gets thrown in practically for free.
But that too should be an outcome of horsetrading at peace conference tables back in the 18th century. Which would I suppose make Iceland another candidate for the North American colonial Committees of Correspondence and Continental Congress to try to recruit to the American Revolutionary cause and allegiance, along with Quebec, the Maritime Provinces, and the island colonies. I guess Iceland would give the Rebels a pass the way those others did--this might be an early link of Iceland to the Upper Canadian Loyalist settlers too, I guess.