I mean, sure — you can see the Stalinist purges as being a form of paranoia, about "wreckers" and about "Whites" and "Trotskyites" and "kulaks" and even "engineers" (as a separate social class that didn't always see themselves as "Soviet") and so on. From the end of the Russian Civil War (1922) until the dead of Stalin (1953) there were waves of purges, persecutions, and so on. It is so core to the early Soviet experience that it is strange to have to bring it up; it was far more extreme, bloody, consequential, and extensive than McCarthyism.

If you are asking, did they ever suspect their members of government were Western spies? My feeling, and it would be good to get others' views of this, is that this is not quite the framework in which they saw things. The Stalinist fears were more along the lines that internal elements were trying to degrade the system in a way to advantage some kind of shadowy non-Soviet powers, not so much the "Americans are trying to infiltrate" framework. The absolutely worst-treated were not people who were suspected to be capitalists or democracy-advocates or spies, but people suspected of belonging to rival Communist groups (e.g. Trotskyites or Mensheviks) or people who were suspected with harboring generically anti-Soviet attitudes.

Oh yes, but not called democratic, just different terminology. There's a ridiculous amount of literature that goes over this; I like A Biography of No Place by Kate Brown, as it very accessibly shows how the Soviet system went from an idealized (and perhaps even innovative, if you consider the time period) nationality policy, to the Stalin era.

Not that distrust of foreigners/spies/what have you was unique to the Soviet time (although it was unique in how systemized/professionalized it all was, as well as the basis/justification on ideology), but you specifically asked about the USSR.