Yeah I don't think it will either. An ARP will survive zone 5/6 which is what the south facing brick wall is.
I should cut it all down and dry it all for cooking. But I can't bring it inside. I have evil rosemary loving cats. I've brought in 2 rosemarys so far and every time the one cat nibbles them to death. Rooting a cutting might work...since I can keep it on a small shelf high above kitty jumping abilities.
