I actually don't have a copy of the confederate constitution handy. Could you post the actual verbiage so we can see what it says?
Not that it matters to the discussion, the *US* constitution does not prohibit secession, and even if the Confederate constitution did, it's still overridden by the natural law right of states to be independent if they wish.
The Confederacy likely wouldhav3 broken up. Texas would have left.