I would see the Russians dealing more with the CSA than the US.
That's not an unfair assumption, though I would suggest that (since the CSA itself is another slightly-backward agrarian nation trying to bootstrap it's way into the 20th century, despite the lingering effects of a Red Rebellion AND a more advanced, rather angry neighbour making it highly dangerous for them to be caught 'gun-running') in terms of pure
realpolitik it makes far more sense for the Russians to approach the United States - not only because they have a land frontier across which to smuggle goodies, but also because the United States is fantabulousy rich & powerful (not to mention free itself of pesky arms-limitation treaties, in theory
and in practice) and potentially in the market for a new European/Eurasian power who can handle the British Empire while the USA deals with problems closer to home - given that Germany signally fails to do very much at all in its ally's favour between the Great Wars (Even if the USA isn't willing to drop Germany in favour of the Russians, there's still the possibility of Russia using an approach to the USA to bring about a rapprochement with Germany without first being forced to go cap in hand to Kaiser Wilhelm - by no means an unattractive prospect, given the caning Russia took as a member of the Entente).
Besides, the Confederate States of America already
have Mexico - why back Russia from all the way across the Pacific when your very own crumbling, Old World monarchy is sitting right there in your back yard, hand out?