No, I don't think it was coincidental at all. FDR was as red as the baboon's tuchis and absolutely adored his uncle Joe. We're lucky we didn't have a hammer and sickle on top of the White House between 1933 and 1945.
As far as hammer & sickle, effectively we did (& still do).
Remember that FDR's 'solution' to the depression was the alphabet soup of gov't run, collectivist & socialist organizations that sought to control every aspect of business & agriculture. Legacies of farm supports, restrictions on what can be grown, labor unions, gov't intervention in the economy are with us today.
When the supreme court ruled against some of his measures, his planned response was to pack the supreme court. Unfortunately, the SC backed down. Kelo is a direct result of this unconstitutional legacy.
Remember also the context of the post-12/07 world. America is attacked by Japan at Pearl Harbor, so our main target becomes Germany (who coincidentally had launch a major attack on mother Russia 6 months earlier).
However, despite Roosevelt & his advisors being obviously communist or openly symps (perhaps at best "naive"), it probably WAS the best deal that could be gotten at Yalta.
The Red armed forces were much larger and stronger than ours (compare man power of the Eastern Front vs. Western Front). Their tanks were better (T-34 could take a Panther or a Tiger sraight up, the Sherman needed a 4 - 5 tank advantage). Their artillery was more numerous (always a Russian strong point) and they had an effective assult rocket capability. Tactical air would be about evenly matched. The Red army had a three year advantage in battle field experience to draw upon that our forces were still learning (our only main battles after D-Day period were the Ardennes & Hurtigen forest [both of which resulted in allied victories but at a high cost] and the Arnham disaster).
The only clear advantage that we had was in strategic air forces. However, the Russian targets would have been out of range of the B-17s & B-24s in England & Italy. We would have had to reallocate B-29s from the Far East to strike at the Russian industrial base. There would have been major work needed to lengthen the run ways to support the newer aircraft.
Although I am a fan of Patton, he would have come out second best for the reasons listed above. The main Soviet thrust over the North German plain would have hit Montgomery. Monty couldn't best the German's second string in North Africa without an overwhelming superiority in men & machines. He would have been over run quickly by the Soviet varsity (followed by a retreat to the port of Antwerp). The front lines would probably have stabilized in the lower Rhine with the Americans perhaps holding onto the highlands in Hessen & Bavaria.
The most charitable thing that has been said about Roosevely at the conference is that he was a tired, dying man who hoped for a better world.
FDR was a Commie stool pigeon and a socialist.