I don't know how Georgians were viewed in Stalins era, I was born way after that. But when I lived in Soviet Union, I remember that Georgians were looked down to. Mostly because of their funny accent and bad "Russian", imagine that. In addition to that, the Georgians that ventured from Georgia into the Russian lands were "speculators", the ones that brought oranges and other exotic fruit to sell on semi-underground farmers markets.
If your story is set in Stalin's era on Russian territory, Moscow or Siberia, etc. there were very few Georgians amongst russians. So, in Stalin's era, I imagine, these few were more educated, most likely members of the party, and they would have been respected. I guess, people would have to stop and really listen to what the Georgian would say, in order to understand him. I specifically said, "him", because there would be very little chance of Georgian woman being outside of the family in a foreign (non-georgian) territory.
Regarding this, "Stalin himself was not as popular in Georgia as he later became." you have to understand that occupied republics hated Soviets (Russians). Since Stalin was a Soviet, there you go.