You can tell there's a magnetic field, certainly. My argument is essentially one of nomenclature; I don't feel a constant electron-field should count as 'flowing'.
Of course it isn't actually constant -- there are multiple electrons, and you can tell that the electron field is quantized. But the degree to which that is visible, is the exact degree to which the superconductor nevertheless doesn't superconduct!
Of course it isn't actually constant -- there are multiple electrons, and you can tell that the electron field is quantized. But the degree to which that is visible, is the exact degree to which the superconductor nevertheless doesn't superconduct!