If you are playing against an elite player, what you do with the British will determine, in my opinion, if the allies win or not.
1. Yes, you have to do some type of invasion/or more likely a raid of either France or Italy. You have to land at least 3 units in France or Italy. Most likely Sicily. This will lead to 10000 point increase in morale for the Russians. This cancels out lots of the early morale losses that the Russians suffer from losing cities, units, and territory. So this is a big deal.
2. Lots of axis players are completely focused on destroying Russia, so defenses are relatively weak in France usually.
3. Use special forces, cavalry, or AA unit for the invasion. The later units are cheap, the SF unit can withdraw through amphib transport.
4. If you are lucky, you can capture a port and send more units if your opponent is slow in reacting to the allied raid.
5. It is possible to mount a more significant overlord operation in France if you focus on building units early. Example. While defending France build British para unit to defend England, but then use it for the raid in 1941-42.
6. If you invade France with the 3 units at the end of 1941 and they are still there at the beginning of 1942, then the Germans don’t get to build the beach fortification of the Atlantic Wall. This is super gamey, but I promise you, all the veteran players are taking advantage of any quirks in the game.
7. Any invasion or raid of France or Italy also lowers the national morale of those countries too. This is especially true of Italy, in the event of invasion of its territory.
Other options to help the Russians
1. Conduct raid into the German Baltic Sea by taking Copenhagen or landing special forces units north of Hamburg or the square west of Copenhagen. This allows Royal Navy to charge into the Baltic Sea and to try to destroy the German Navy that is at sea there or in Port.
2. Seize Narvik with allied forces per that decision point in 1940. This really helps secure the Murmansk convoy. You have to send more forces though to take the place from the crazy elite garrison unit that shows up there.
3. Get the British Bomber lots of experience by having it hit ports in France or Norway in the later part of 1940 into 1941. Then with it at elite level, start hitting all of the German industries in the summer of 1941. Have to have fighter cover for the bomber and have upgraded British HQ.
4. If your opponent fails to garrison Holland correctly, if you take The Hague and Amsterdam, most of the time you can capture the port intact at 5 supply. You then transport units right into Holland and try to get as far in as you can. This will not give you the 10000 point morale boost, but it will cause the Axis to pull units off of the eastern front pretty fast in my opinion.
I hope this helps,