I honestly don't see how they're going to defend this in court under UNCLOS. It's really a pretty shaky position ... If anything, Denmark appears to have the best claim to the geographic north pole.
Traditionally, when two nations' EEZ's or territorial waters limits interfere with each other - take for instance the Straits of Juan De Fuca, between Washington state and British Columbia - they are divided straight down the middle at a point equidistant from each nation's shoreline, so that half the water belongs to one, and half belongs to the other.
The Northern tip of Greenland appears (from my map - 1954 Brittanica World Atlas) to be closer to the North Pole than any Russian territory. But, maybe there's been some new land springing up since 1954 that I don't know about ...
Anyway, dividing the territory on the north pole between the nations that own land north of the Arctic Circle according to UNCLOS, I'd say Denmark gets the actual Geographic north pole, and Russia gets some stuff close to it, but not -on- it.
I don't think Russia is gonna back down from their claim, though. They've made it very public already, and it'll be a matter of national prestige to keep forcing the issue.