Yes, it definitely had an impact, and this impact was fully intentional on the part of the policy makers. The USSR enforced what was intended as a cultural melting pot on the indigenous majorities of the soviet republics. In practice, these policies ended up meaning a continuation of the russification policies of Tsarist Russia, under new ideological auspices.

Comparisons to the EU are, however, not as straightforward. What took place in the USSR was not a symmetrical, market-driven labor flow, but a top-down policy of encouraging the migration of culturally and ethnically Russian labor into the other republics, and creating large Russian minorities (and eventually, majorities) in those territories. The USSR funded a great deal of industrial development (particularly heavy industry) in the Baltics, but instead of having this industrial development lead to the indigenous populace moving away from agrarian careers and into industrial ones, the new industrial facilities mostly employed immigrants from the Russian and Ukrainian Soviet Republics. Meanwhile, the indigenous population was practically forced to remain in the agrarian sector, which saw far less funding from the central government of the USSR. There was also the issue where the USSR continuously neglected the development of food processing industries in favor of heavy industry, once again limiting the prospects of the local population.

Soviet colonialism in the Baltic states: a note on the nature of modern colonialism
V. Stanley Vardys, 1964