First off, the Battle of New Orleans was fought after the Treaty of Ghent had been signed and changed nothing about the terms. As for U.S. independence, that had been accepted by the British in 1783, so there was no change from before the war, and I can't recall ever seeing the British contest the Louisiana Purchase. Certainly the Treaty of Ghent makes no mention of it.
If the Brits had won New Orleans, the unratified treaty would have been out the window.