Admiral Gorshkov was a very progressive Soviet thinker, he wanted a blue water navy and helped build the Soviet fleet into what it was during the 60s though to the end of the Soviet Union, a fleet capable of challenging NATOs combined might. He did have plans for aircraft carriers but politically they were unpopular as being too expensive to design, build and there was fearsome fighting between the airforce and navy.
The Soviet Airforce said it could support the navy with long range bombers and do anything a carrier could do without the initial expense of building and maintaining carriers and thats what the Politiburo went with.
If Gorshkov had managed to get his way and convince Kruschev that missiles were not the sole defender of the Soviet union, then you could quite probably see Soviet Carriers beyond the small Kiev class, or have the Kiev's as proper carriers rather than missile carrying hybrids. Maybe if he convinced the Soviet leadership that carriers could be used as mobile missile bases that could strike anywhere in the world then you might see it. Its more possible than folks think.
One thing I just remembered, the Soviets in terms of surface ships seemed to build things in steps. A case of 'lets build this, did that work? Yes, then lets build an improved version.' I say this because you only have to look at the evolution of soviet carriers to get this feeling. They started with the Moskva class helicopter carrier, then went to the larger (but still small) Kiev class and their fixed wing compliment, then there was their successor, the larger and never completed Ulanoskv class carriers and the smaller Kusnetzov, the current carrier in service with the Russians which was the successor to the Kiev class. This all is very logical progression and development steps. So even if you got Soviet carriers you might see them taking baby steps.
If they had managed to keep the Graf Zepplin and study it and saw the need for carriers that also might have influenced things in Soviet thinking.