Good theory - but just as an fyi, she did pass through the wall to burn Mance and accept the wildlings:
"Beneath the weeping Wall, Lady Melisandre raised her pale white hands. "We all must choose, " she proclaimed. “Man or woman, young or old, lord or peasant, our choices are the same.” Her voice made Jon Snow think of anise and nutmeg and cloves. She stood at the king’s side on a wooden scaffold raised above the pit. “We choose light or we choose darkness. We choose good or we choose evil. We choose the true god or the false.”
Mance Rayder’s thick grey-brown hair blew about his face as he walked. He pushed it from his eyes with bound hands, smiling. But when he saw the cage, his courage failed him. The queen’s men had made it from the trees of the haunted forest, from saplings and supple branches, pine boughs sticky with sap, and the bone-white fingers of the weirwoods. They’d bent them and twisted them around and through each other to weave a wooden lattice, then hung it high above a deep pit filled with logs, leaves, and kindling."
…
“Come,” urged Melisandre. “Come to the light … or run back to the darkness.” In the pit below her, the fire was crackling. “If you choose life, come to me.”
And they came. Slowly at first, some limping or leaning on their fellows, the captives began to emerge from their rough-hewn pen. If you would eat, come to me, Jon thought. If you would not freeze or starve, submit. Hesitant, wary of some trap, the first few prisoners edged across the planks and through the ring of the stakes, toward Melisandre and the Wall. More followed, when they saw that no harm had come to those who went before. Then more, until it was a steady stream. Queen’s men in studded jacks and halfhelms handed each passing man, woman, or child a piece of white weirwood: a stick, a splintered branch as pale as broken bone, a spray of blood-red leaves. A piece of the old gods to feed the new. Jon flexed the fingers of his sword hand.
