No, like the Trabbi, it became somewhat of a joke to the western communists. They wanted Soviet Style Communism, but of course "they" would not have to drive the trabbi or Lada (they woudl continue to get the West German Cars). It is telling - in that she reveals herself to be a campus Stalinist. Fortunately for her, it is not illegal in the west.
But this reference of both Chevy to the Lada is still quite remarkable. They are doing this health care to supposedly help the middle class just like the Russians created the Lada a car for the middle class (really the upper lower class). I see too much insight rather than randomness to think that it was on purpose.