Almost certainly; US leadership (i.e. most elite opinion) was critical and fearful of Nazi Germany. The US entered the conflict by direct support of Britain without any direct attack or threat to the US. Strict isolationism was confined to a small but passionate minority. Nazi triumphs in 1939-1941 brought most Americans to the view that the US must help defeat the Axis, even at risk of war; though even so, only another small minority wanted the US to join the fighting.
An outright Nazi-Soviet alliance would be even more threatening. Also, it would alienate or demoralize those Americans who sympathized with either state (such as the Reds who promoted isolationism at Soviet direction until BARBAROSSA). I think it would be harder even for them to swallow such obvious hypocrisy.
There were some who were hostile to only one of the two states, and OTL willing to let the other do the fighting against it. ITTL, anyone hostile to either state would be hostile to the alliance of them.
As noted, Japan could be excluded from the Axis, as being in conflict with the USSR. Japan could then become a co-belligerent with the Allies, as the USSR did OTL.
OTOH, Japan and the USSR could partner in dividing China, and with Germany in seizing the British, French, and Dutch colonies in SE Asia.
One factor: the Axis was officially the "Anti-Comintern Pact", so the USSR has to stop being Communist. It would be awkward for the USSR to adopt "National Bolshevism", as Stalin was not Russian. (And because so much of the Soviet population was not: volksdeutsch, Tatars, Kazakhs, Bashkirs, Kalmucks, Uzbeks, Georgians, Armenians, Samoyeds, Karelians, Jews, Chechens...)