Sverdlov construction could have triggered a postwar cruiser race

Could the Soviet Union engage in a qualitative cruiser race after the Second World War?

Yes. The Sverdlov class was a good 1950s cruiser, and building the proposed numbers would have produced a real race.

The Soviet Union possessed a viable 1950s gun-cruiser design in the Sverdlov class rather than merely an aspirational paper project. The ships were good enough to be taken seriously by Western navies. If the large planned program had continued, the issue would have become quantity as well as individual quality. Credible mass production can create an arms race even when a ship type is not revolutionary on its own.