Assuming for the moment that the abolition act takes place at the same time as OTL (in short, granting the PoD), then... well, in the first place it's possible that slavery is less important to the South than it was OTL (as abolitionism got rolling a lot sooner in the British Empire than it did in the US).
Basically that's a big part of it. It might be only the deep south secedes, it might be every colony corresponding to an OTL state which had slavery, or it might even be every colony corresponding to a state which still had slavery in the 1830s (which is... pretty much the same).
Texas won't be there, most likely, I can't see why it would be annexed to BNA. But perhaps the more important matter is that such an ATL rebelling south BNA is going to get stamped on hard. (Assuming a reaction speed similar to that of the Crimean War, you'd functionally have 24 reinforcement battalions in theater inside four months - on top of whatever's already garrisoning BNA, which for now I'll estimate as being six battalions).
Even if this alt-South (and BNA North) musters as many men in the 1830s as it does in the 1860s, then imagine a battle the equivalent of Bull Run but with the "North" having an extra two bonus regular infantry corps.