If they manage to hold them into the Cold War that's really going to screw things up regarding the GIUK gap, Soviet ability to base their subs out of the southern Icelandic ports Fabilius mentioned would be a serious threat to US reinforcements being shipped to West Germany. Not sure what sort of knock on effects that might have.
I doubt the Soviets would control Iceland and Greenland after the Revolution.
It's likely problematic, but I'm suddenly imagining a scenario where Russia buys Iceland at some unspecified point, and then after the Russian Revolution Iceland becomes like an early 20th-century version Taiwan, with conflicts between recent arrivals who came with the monarch, Russians who had been there beforehand, and whatever's left of the original Icelanders playing the role of the native Taiwanese...If there's a Revolution.
in the event it goes along the lines of OTL, then the British seizes Iceland, Canada seizes Greenland, and Norway gets Svalbard, and maybe any surviving Royals can flee to it.
It's likely problematic, but I'm suddenly imagining a scenario where Russia buys Iceland at some unspecified point, and then after the Russian Revolution Iceland becomes like an early 20th-century version Taiwan, with conflicts between recent arrivals who came with the monarch, Russians who had been there beforehand, and whatever's left of the original Icelanders playing the role of the native Taiwanese...