If one could pass all the hurdles to a Soviet-controlled Alaska-that Tsarist Russia could hang on to the territory, that it wouldn't break off on its own steam as a refuge for some kind of Whites, that neither Canada (ie, still at this point, basically Britain) nor the USA succeeds in splitting it off as a puppet protectorate--I think one thing Soviet Alaska could not be is a Gulag!
It still borders on Canada. It would be too easy for disgruntled Soviet citizens there to flee individually, or even rebel en masse with some kind of Western support. On the contrary, the place would perforce become a Potemkin Village, a showcase to the world that has this one piece of Soviet Russia to scrutinize from close by, that the Soviet system works and has won the unswerving loyalty of its liberated worker-citizens of the first Worker's State. The Kremlin might have to devote really inordinate resources to transfer there, to keep the Soviet Alaskans happy and loyal. Then of course the Soviet regime, if could possibly manage to afford this extravagance, could possibly open, or at least relax, its border, let foreigners visit and leave freely to spread the word that Leninist Socialism works!
But I'm not in the least sure that the Soviet Union could manage that sort of force-fed showcase province in good time; as things were OTL economic development was touch-and-go.
Also I do think that's a lot of gauntlets to run, to have Russian Alaska wind up in the secure possession of the Red Kremlin like that.