I agree with Tony about differences among people's limiting magnitude measurements. There's a 0.8 magnitude difference from when I'm not wearing my glasses to when I am.

On the other hand, that's only because the stars tighten up and fainter ones become visible as a result of the sharper focus. The visibility of large diffuse objects like the Milky Way doesn't really seem to be affected. Other people's experiences may be different.

On a good night from my back yard in the red zone (Bortle class 6.5 and a limiting magnitude of about 5.3 for me) I can see the Cygnus star cloud and some extremely faint traces of the Milky Way extending to around Albireo. That's it.

From the site I use about 30 minutes away in the orange zone (Bortle class 5 or so with a limiting magnitude of about 6), the Milky Way is extremely obvious and stretches from Sagittarius near the southern horizon to the southern end of Cassiopeia; and the only reason it's not visible farther north is because of the light dome from Youngstown. M31, the Double Cluster, M7, M8, M24, Mel 111 and - I think - the North America Nebula are all clearly visible.

The Milky Way from this location is nothing like at an extremely dark site but it's still very easily visible, while at my suburban site with a NELM just 0.7 magnitudes lower it's hardly visible at all. I think for the Milky Way to be more than just a vague hint you need a NELM of close to 6, if you have perfect vision or are wearing glasses to correct it.