People keep asking how will america react, but what about Canada, who is actually sharing the border. Someone said earlier that the border settlement between Alaska and Canada would be different and their probably right. The deal was a big stab in the back for Canada since for the settlement, America got three judges, Canada two, and Britain one, and the good ol'motherland sided with America for political reasons, and Canada just fumed.
Also, if some form of World War II breaks out, would the Americans just leave it to Canada, and if Canada did deal with it, would their be any chance for anexation. I wouldn't be surprised if Ottawa would be for annexation, since Canada didn't stop growing until after Newfoundland joined in 1949.
I don't know about the United States, but Canada was an absolute dick to the Japanese-Canadians during the war. Even when a police enquiry said they weren't a threat, we confiscated their fishing boats and other property (which was then sold off for well under their actual value), deported many and moved others to nasty internment camps in the interior. So if Canada did annex Alaska, the Japanese natives might not be so well treated. And even if Canada didn't annex Alaska, all those nasty things the government did to the Japanese-Canadians was out of fear of a (improbable) japanese invasion. With a Japanese Alaska at war with Canada,(if war did break out) expect the treatment of Japanese-Canadians to be much worse.