My apologizes. I'm not deleting my response, but I just saw that this has to be done before December 1941.
In that case the answer is no. The furthest east the Germans got IOTL in 1941 was Rostov, and they were promptly kicked out of there, and Rostov is nowhere near the Volga. And just securing the south Ukraine required a massive diversion of forces from central Russia.
The Germans could have gotten further in the Ukraine, but "gotten further in the Ukraine" means being able to hold Rostov and Kharkov in the face of the Russian counter-attack. There is also a point where they would have had to stop and wait for the rail lines to be repaired, and I suspect that this point is well short of the Volga.
Maybe with a complete collapse of the Soviet Union, after the new treaty there is a German occupation/ observation force on the Volga, but then why would this force cut river traffic?