IMO even with heavy propaganda any CSA free election that covers all/most of the old US would very likely result in some kind of socdem that may have been radical in the old US but very much extremely moderate by the standards of the CSA, perhaps even reactionary depending on who you ask. And I'm not sure if the events ever mention any activity by a democratic party more right wing then socdem, surely there would be at least a few liberal/conservative people getting elected even if they dont have the numbers to really do much.The west coast in fact had a lot of labour activity OTL and the fact the PSA sweep that under the rug should probably lead to it bubbling up all at once when the CSA walks in.
I didn't really think about how they'd run territory they had to reconquer late in the war though, so that's my bad. I expect what I said to be mostly correct in the territory they start with or quickly liberate from the federal junta. The south is very likely to undergo something akin to the aborted plans for reconstruction, with disenfranchisement of planters and a lot of state support for CSA leaning black people to break the reactionary domination that lead to the AUS in the first place.
Now dont get me wrong, despite what this convo has been like I am very much a CSA fan, admittedly primarily for their social views, but I am not going to pretend they are perfectly democratic when they very clearly are not.