IMO it is not very likely, primarily due to the extent to which the Soviet bureacracy was corrupt and almost pathologically resistant to change. The main reason IMO for the Soviet Union's breakup, apart from the economic reasons, was that the second strong central government weakened, every party leader in their appropriate parts declared either complete independence (like Kravchuk did in the Ukraine), or effectively created a little personal kingdom that, while paying lip service to the government in Moscow, effectively ran its own course. In fact, much of the former USSR is still ran by the former party bosses, although under different guises.
In fact, much of the USSR during its heyday was ran almost solely on informal network of party bosses in various parts of the country rather than on a strong central government that could pretty much disregard whatever the regional leaders had to say. When the central government was strong either due to a powerful leader, or due to the Politburo's complete control over the army and secret services, any attempt at secession would have been eradicated by force - however, with Gorbachev being a weaker leader, and with much unrest in the party hardliners, it would have taken an earlier change... possibly during Khruschev's rule, when the so-called "ottepel'" ("warming up", literally) started. Had Khruschev been able to restrain the hardliners during his stay in power, and had he been able to retain power for ten additional years or so, he could have started to slowly replace hardliners in positions of power with trusted reform-minded individuals, which by Gorbachev's time (or by the time of someone like Gorbachev) would have resulted in the local and regional governments following through with commitment to reforms as opposed to trying to create their own private kingdoms.
Another factor in the USSR's demise was that instead of completely replacing regional power structures, Russia (and later USSR) effectively adopted them and fitted them within USSR's framework. In other words, a semi-tribal chief in, say, Abkhazia would still retain his power, possessions, and authority, except instead of being called a chief he would become a local communist party functionary. As a result, many parts of the former USSR, especially outside of big cities, were ran essentially in the same way they were ran for hundreds of years before, and the local population's loyalty to their own locally made leaders was greater than to the central government in far-away Moscow.
In the areas with a stronger nationalistic streak (like Ukraine - I am bringing up this example since I lived in the Ukraine during the final days of the USSR, and am somewhat familiar with what was going on firsthand), even if the social structure was more developed, the informal network that helped those in power to maintain control over regions of the country was also the undoing for the central government in Moscow, as in the hierarchy of Soviet power leaders of separate "republics" were responsible to the party bosses in Moscow; the regional leaders were responsible to the leaders of the "republics", and local leaders were responsible to the regional ones. Effectively, if the leader of the "republic" decided to go his own way, and the government in Moscow was too weak to effectively act, he would inherit the entire hierarchy under him, who would respond to him and not to the central government of the USSR.
So in order for perestroika to work, it would have required cooperation on every level of the government - within the Soviet structure as it was by the 1980s it was nearly impossible. The change would have had to start in the 1950s or 1960s at the latest to come up with a much more centralized USSR by the 1980s where no subordinates would be able to break away and form their own little kingdoms without fully knowing this would have resulted in their absolute destruction.