Yes, Stalin knew FDR was reluctant to be Churchill’s useful idiot.
From Terehan on Churchill became the very junior partner in the Alliance. Best example was FDR’s hesitance, bordering on refusal, to use 8th and or 15th AF to aid the Polish Home Army’s Warsaw Uprising. Churchill used RAF elements to airdrop supplies but Stalin refused landing rights to aircraft aiding the Poles so amount of supplies was very small. FDR said he did not want to upset Stalin before Yalta even though that was seven months in the future. Speculation has always been made about that FDR Stalin meeting given subsequent events.