For example, since the RSFSR in our timeline had no anthem nor a branch party of the CPSU and KGBT of its own, and most of the institutions were under direct control of the central state of the USSR, what if Khrushchev or Brezhnev had introduced them, would it have influenced the course of USSR history in any way?
Nothing? Like absolutely no change what so ever, till you get to Yeltsin you will just have one more layer of leadership in the CPSU and KGB. The leadership of the party is still paramount as the regional leadership is still answerable to the central leadership in Moscow and they are monitored by the central leadership, they are appointed by the central leadership in Moscow and no policy decision can be taken that is not in line with the policy of the party cause you are not introducing democracy, free speech and free and fair election all you are doing is appointing some paper pushers who would take on some responsibility of what would have been handled by the central leadership . In fact you might see some moderately better administration since the central leadership is not overburdened with internal matters of RSFSR as it would be taken care of by the local leadership.
Once you get to Yeltsin, things will get interesting....... remember most of the deputies in the Russian parliament supported Yeltsin in his consolidation of power from 1989-1991 because of rapidly changing situation in the Union and in the RSFSR including the infamous parade of sovereignties where even ASSRs of RSFSR were declaring sovereignty and threatening the territorial integrity of RSFSR and the CPSU did diddly squat. This made the deputies even the CPSU loyalists in the Russian Parliament nervous and so they broke ranks and gravitate to Yeltsin and abandoned Gorbachev cause he was doing nothing to protect the territorial integrity of RSFSR and Russian interests the so called "What about the Russian Interests?" and mind you some deputies who backed Yeltsin in his power consolidation were conservative communists who had sympathies with Russian Nationalism saw Gorbachev as ineffective.
So if the RSFSR is indeed administratively autonomous from the Union, you might see the rise of a conservative Russian communist (in our time line a lot of RSFSR deputies were hardliners) who would oppose the liberal reform of Gorbachev and the Parade of Sovereignty and might try to rein in these declaration. Basically Yeltsin has competition and he would not be in a position to consolidate so much power and rise in opposition to the power of the union Centre, we could see RSFSR branch being the focal point in opposition to Gorbachev's reforms which might require Yeltsin and Gorbachev to work together to break the hold of the conservative in RSFSR congress of people's deputies and the RSFSR branch of CPSU.
