Yeltsin was definitely a factor, but the presidents of the other constituent republics also wanted to get rid of the USSR. There was a wave of nationalism at the time. Almost every republic saw its best interests were to ditch the USSR. According to the laws of the Soviet Union they could do this, and they did with the Belavezha Accords and the Alma-Ata Protocols.
Probably anyone succeeding Yeltsin to the presidency of Russia would also want to do the same thing.
Yeltsin had his base on power in the Russian SFSR. Gorbachev was ruler through the Soviet government that was above the consituent republics. Eliminating that supranational government was a way to eliminate all power Gorbachev had over him. That's a powerful incentive for anyone who succeeds to Yeltsin's position.
The 1977 constitution of the Soviet Union gave individual republics the right to secede from the USSR. Like many "ideals" enshrined in Soviet law, this was not mean to be taken seriously, but only for outside consumption to fool the gullible. But it did give the basis for people to legally leave in 1991.
Ukraine, Belarus, the Caucasus, and the Baltic states were all going to leave the Soviet Union regardless of what the Russian SFSR does. When they do, there is complete duplication of effort: the Soviet government and the Russian SFSR completely overlap. If you are in the Russian SFSR, why not leave the Soviet Union and have complete power yourself? Once Russia is not a member of the Soviet Union, what possible role can the Soviet government play if it has no constituent republics? The Russian SFSR will then seek to become the legal successor to the Soviet Union.
The only real change is who leads Russia after 1991, and whether he can do a better or worse job than Yeltsin.