The ideals of Illich's work are so far removed from the centralized, institutionalized Soviet socialism, I really doubt the Soviets would've been very happy if people in the USSR started talking that way. Anyone who is swayed by Illich will loathe the idea of five year plans, concerted efforts for more technological progress, and the propaganda that goes with it ("Plan is law, fulfillment is duty, over-fulfillment is honor!").
But who knows, maybe the communist spooks just saw someone geographically close to the US propounding ideas that were radically different from capitalism and didn't mind that they were also radically different from communism. The same has happened enough times in the other direction.
I really see Illich idea fully orthogonal to USA capitalism vs. USSR weird communism flavor. They can be applied in both in different directions
Usually the idea of critique was to create dissatisfaction with democracy, not to advocate for what the USSR was doing. For example, the KGB heavily promoted the US peace and anti-nuclear movements despite being strongly pro-war and pro-nuclear within the Soviet Union.
It's a bit like the fundamentalist religious people who talk a lot about how immoral everyone else is but then make excuses for the immoral things their leadership is doing. Or the congresspeople who talk about how important the family is but are serially unfaithful and don't see their kids.
It's more about having a useful way to attack people than an advocacy for a specific position or way of life.