This is all before the Communists took over and they had a good, strong leader in the Czar. When World War I started, Russia and the USA should have immediately started mobilizing like they were getting ready to attack the Central Powers. When the rest of the Allies start bugging them for help, they keep saying they're mobilizing. They keep it up for a few months, the Allies are kind of getting their asses kicked, and then Russia breaks off ties with the Allies (USA hadn't joined yet), makes peace with the Central Powers, and the USA and Russia invade Canada out of nowhere. After conquering Canada, they conquer Greenland and then Iceland.
Neither the Allies nor the Central Powers would have done anything since they would have been mired down in war. Denmark would not have bothered defending Greenland. Afterwards, smashing Iceland would not have been hard.
Russia would get the top half of Alaska back and the USA and Russia would split up all of Canada, Greenland, and Iceland, with the USA getting a bit more of it since they were giving up the top half of Alaska. The Czar would stay in power and the Communists would not take over Russia. Everybody would have won.
Are you for real? Russia should have stayed out of a war that they basically started? America mobilised? In 1914 the US had a tiny army (compared to the European powers of the time) and no process in place to build a mass army, or to supply it, or to transport it or even fight it. When the American expeditionary force arrived in Europe in 1917, it was forced to use British and French weapons and equipment. Invade Canada? ROFL!
Even though we joined the war in 1917, we mobilized 4.8 million military personnel. Canada declared war in 1914, and only mustered 600,000 troops. Here's why. The population of Canada was 8 million people in 1915. The population of the USA was 92 million.
With Russia and America switching sides to the Central Powers, Germany would not have been fighting a two front war.
Perhaps not Germany, But Russia and America would. Remember Japan was on the side of the UK and France, and Japan's navy was very efficient and had recent battle experience. You are also forgetting the possibility of an attack from British India against Russia. An American war against the British Empire at that time may not have been such a pushover as you might imagine. Anglo French fleets bombarding American cities on the East Coast and Japanese Fleets bombarding American cities on the West coast, not to mention amphibious raids to tie down American forces and your 4.8 million is suddenly a lot less to invade Canada. Forget Greenland and Iceland. This whole premise is silly. America did absolutely the right thing in WW1.
So basically, take World War I and leave both sides alone with two exceptions. Both the USA and Russia switch sides and help the Central Powers instead of fighting against them. Second, the USA begins mobilizing immediately. I fail to see how this would not have significantly harmed the Allies and I also fail to see how it could possibly have helped them.
The Schlieffen plan would have been implemented with hundreds of thousands of German troops brought over from the Eastern Front along with a million or so troops Russia rushed to the German border being thrown on German trains to provide additional reinforcements in the invasion of France. Also, Germany would be trading with Russia to lessen the effects of the British blockade. There would not be hundreds of thousands of Canadians helping defend France. Austria-Hungary could focus entirely on Serbia from the beginning and smashed them decisively at the beginning, as they would not have been attacked by Russia on account of Russia having their eyes towards carving up Canada.
The USA and Russia would not be trading with England and America would disrupt Canada's attempts to do so. There would not be thousands of Americans on British passenger liners and there would be no American merchants trying to trade with England, so Germany could utilize unrestricted submarine warfare throughout the entire war. This would have been disastrous for England's trade. Turkey would not have attempted their idiotic and catastrophic winter invasion of Russia.
After Russia helped Germany smash France while America mobilized, Russia and America would finish off Canada.