No. Russian SAMs are massed around Moscow, St. Peters, and other major cities. There isn't even a continuous radar coverage over some parts of the Far East and Siberia, much less continuous SAM coverage. However when you take into account the Land Forces SAMs, and fighter CAPs, they can effectively provide air cover over the conflict zone. They just can't do it everywhere at once.
What exactly do you mean by modern? The MiG-31 primarily faces Chinese Flankers, and MiG-21 derivatives. They are not any more modern then any MiG-31BM. With those kinds of fighters, it can still effectively engage Chinese Tu-16 clones, should they attempt to strike targets deep inside Russia, and disengage before the escorts can close.
They exercise with AEW aircraft fairly frequently these days, but I don't know if there have been any major improvements in coordination with GBAD. The brand new Barnaul-T is supposed to address that exact problem, but so far it's only been delivered to the 18th Motor-Rifles, in Chechnya, for experimental exploitation. It allows integration of all brigade level IADS assets into a single system, and can communicate with VVS assets. I imagine once the Barnaul-T, and other automated C4I systems, are delivered in quantity we will see a marked improvement in that department. For the time being there is marginal improvement on that front.
