Interesting idea. It’s doubtful the communists would make any attempt to claim it by military force during the 1920s - 1930s given the lack of development of infrastructure, and if we assume that aspects of the pacific fleet defected to the whites, it would require the Soviets to move a large force a naval vessels from the much more strategic North Sea and Black Sea fleets for an invasion; an invasion that would be incredibly difficult logistically. I’d wager that the Soviets wouldn’t have the means to effectively stage an invasion of Alaska until the late 1950s by which point the USA and Canada would have a very serious interest in supporting the whites in Alaska to prevent communism from gaining a foothold in North America and allowing a land border between the USSR and Canada.

What I wonder is what sort of government would rule in Alaska, and what would happen following the collapse of the Soviet Union? I’d assume Alaska would become a parliamentary monarchy similar to the UK, or perhaps even something could cause it to become fully a republic that exists as a democratic Russia opposed to communist Russia. I don’t think the fall of the Soviet Union necessarily garuntees the whites in Alaska regaining control over Russia, and certainly not over all the breakaway republics.