Thanks. It is surprising that this was apparently not mentioned in Russian media, considering how unpopular Yeltsin was.
If they did set up a referendum in the area at the time (c. 1993 or 1993), it would not have been at all sure that the majority would have voted for staying as a part of Russia. Karelia is not a terribly affluent area even in the Russian context, and many people might have felt that becoming a part of Finland would be the better choice in economic terms.
A referendum is of course a different matter. From the way this plan of Yeltsin was described, I assumed that a referendum was not considered.
And while Finland certainly would be attractive to the inhabitants of Karelia in the 1990s, higher standards of living do not always mean that they would want to join another country. See above the example of the Kuril islands, where despite the much higher Japanese living standards, the population of the islands is overwhelmingly opposed to joining Japan. An important factor is whether the inhabitants think they would be treated well in the new country and the Kuril islanders obviously have good reasons to think otherwise. So it depends on how willing Finland is to welcome the Russians in their country.
The number of Russians depends on what area we are talking about. Finland gaining just Viipuri/Vyborg and immediate surroundings would still only make Russians the second-largest minority. It would be a big minority to be certain, and naturally this matter would be something the Finnish leadership would have to take into very serious consideration.
The population of the former Finnish territories (and I didn't check Sala and Petsamo) in 1989 was about 380 thousands. Just the Karelian isthmus was about 275 thousands. The area around Vyborg might be around 100 thousand. Though one would think that any Finnish leaders willing to reopen the border question would want more than just Viipuri.
As for how realistic such a scenario is, according to the article linked to by Karelian (and provided Google Translate is any good with Finnish) claimed that that the Russian group was in contact with the Finnish president, so it wasn't entirely hypothetical even in OTL. Provided that a Russian government actually did offer Karelia back (in my opinion, a more difficult prospect than Finland accepting Karelia) and the local population agreed, wouldn't it be at least politically difficult for any Finnish leadership to refuse the offer?