Not correct. After the various border incidents and firefights between the Japanese and the Soviets from 1932 to 1939, the two nations signed the Japanese–Soviet Non-aggression Pact on 13 April 1941.
After that, Soviet naval vessels were free to sail from Vladivistok whenever and wherever they wanted. In fact, US-built merchant vessels transferred to the Soviet Far Eastern State Shipping Company, operating under Soviet colors and with Soviet naval escort, delivered a steady stream of goods moved from the west coast of the United States and overall accounted for some 50% of all Lend-lease goods to the Soviet Union (8,243,397 tons). Note that this was all "non-war materials" goods... but included foods, raw materials and non-military goods such as lorries and other road vehicles, railway locomotives and rolling stock.
Note that some 452,393 tons of this material was then shipped north through the Northern Sea Route to western Soviet Arctic ports.
Many military aircraft were flown from Alaska to the Soviet Union across the Bering Sea (often with cargo), and a small amount of war material was shipped through the Bering Sea, avoiding Japanese inspection during the summer months by partially unloading in Petropavlovsk-Kamchatsky to reduce their draught to cross the shallow Amur River estuary and enter the Sea of Japan via the Strait of Tartary.
So yes, a Soviet carrier COULD have sailed the Northern Sea Route to Vladivostock, then operated freely for training etc, including sailing south of the Aleutians, etc... although it would have to have its planned route & schedule provided to Japan to ensure that no "accidents" would happen.
The Japanese–Soviet Non-aggression Pact remained in effect until 5 April 1945, when the Soviet Union announced its intention to terminate the Pact. The text of the Pact required that the Pact would remain in effect until 1 year after termination notice was given... and Stalin declared his intention to honor that year delay. Open hostilities were avoided until the Soviet invasion of Manchuria on 9 August 1945.