You can; the thief just didn’t get to do that because they were busy getting away in a non-conspicuous way.
But even turned off, “Find my” stays active these days (although you can no longer make it ring, I believe).
But even turned off, “Find my” stays active these days (although you can no longer make it ring, I believe).
And even if it does, turning on Airplane mode is not possible anymore for a locked phone.