While there is a slight chance that Kovalchuk will stay in Russia, it's much more probable that he will return to North America after the new Collective Bargaining Agreement is ratified. Technically, the new CBA has not begun yet, so Kovalchuk is doing no harm by staying in Russia a little longer. If he's enjoying it over there, there is no problem with him waiting a few more days to leave. However, we simply do not know what is going through his head. We don't know what he is thinking, or whether he has already made his decision. Devils fans should not prepare their pitchforks just yet.
Remember: Kovalchuk is entering the third year of a 15-year contract worth 100 million dollars that he signed with the Devils in the summer of 2010. He is making A LOT of money playing in North America, and he is currently building a 20,000 square-foot mansion in Bergen County, New Jersey. It is difficult to see the rationality of him wanting to drop everything that he has here and head over to Russia. Even with the statements made by KHL president Alexander Medvedev, where he stated that the KHL intends to keep any players that wish to stay, Kovalchuk has said that he will not make a decision until he "read(s) the new agreement."
Until then, it's all just speculation, but it seems like the media and hockey fans on Twitter are making this into a bigger deal than it really is.