I don't know about SCOTUS, but the AL Supreme Court would probably also say that there is no constitutional right to conceal, only to carry. In the ruling the protects the right to OC for Alabamians, the ALSC said that the State could restrict CC or OC, but not both. They also tended towards OC, since CC is what the bad guys do.
The State chose to restrict CC, so all laws generally restricting carry are interpreted as restricting CC, not OC.
In essence, the laws do not restrict carry. They restrict concealment. For that reason, I would have no objection to any of the games they play with permits--if it weren't for the law requiring a permit to carry a gun in your car. We gotta get that one changed.