No. The Russian Soviet Federative Socialist Republic had a distinct government from the Soviet Union. The RSFSR, between 1917 and 1991, was one state within the Union and had its own leader, though from time to time (most notably in the earliest years of the Soviet Union) the same person held both titles.

It's important to note that when you talk about the "Soviet leader," there's several different offices that you could be referring to. The 1977 Soviet constitution, for example, refers to the Chairman of the Council of Ministers as head of government, while the Chairman of the Presidium was head of state.

Generally, however, we talk about the General Secretary of the Central Committee of the Communist Party as being the Soviet leader. This office controlled both the Communist Party (the only one allowed in the country) and the Soviet government.

Vladmir Lenin was chairman of the council that led the RSFSR from 1917 to 1924. He simultaneously was leader of the USSR from its creation in 1922 to his death 14 months later. He was followed by Stalin, who took over from Lenin in 1924, serving as both the leader of the RSFSR and the Soviet Union until 1929, when he passed the RSFSR to Sergei Syrtsov.

Note that both the Soviet Union and the RSFSR had premiers, and depending on your definition of "leader" ─ whether it's the person who has the title or the person who has the power ─ Alexi Rykov served as simultaneous premiers of the Soviet Union and the RSFSR in 1929 and 1930.