To put it bluntly, it's complicated.

The first thing to keep in mind is that, despite pretty much doing his own thing, Stalin was a Communist. And Communists tend to not be very nationalistic. There's a few notable exceptions to that rule, like the modern Russian Communist Party, but at the time the Soviet Politburo, including Stalin, were not very big fans on nationalism.

That being said, it is clear that Stalin maintained a soft spot for his Georgian homeland throughout his life, and while this sentiment wasn't what I'd call a kind of nationalism, he did play a bit of favouritism with his fellow Georgians. During the Purges, he went out of his way to pardon Georgians accused of anti-Soviet activities and, while many Georgians were purged under Stalin's watch, it was to a far less substantial degree than what was occurring throughout the rest of the USSR. It's also worth noting that Stalin personally appointed a lot of Georgians to key positions within the Politburo, and that many purged officials were often replaced by Georgians. So, while Stalin was not a nationalist by any means, he did have a certain preference and soft-spot for other Georgians.