Even when the molecule is present in a neutral form, as a phenol, the oxygen will still be close to a $\ce{sp^2}$ shape with the $\ce{p}_z$ orbital partially overlapping the $\ce{p}_z$ orbital of the carbon bound to it. The proton NMR of phenol clearly shows characteristic aromatic peaks, demonstrating that the ring is aromatic.
Hückel's rule states that a fully conjugated ring will be aromatic if it has $4n+2$ electrons, and antiaromatic if it has $4n$ electrons, where $n$ is an integer $\geq 0$. The rule is a generalization that comes from how the bonding and nonbonding orbitals are filled as electrons are added to an isolated conjugated ring.
In analyzing the resonance of the phenol, the Hückel rule applies only to the phenyl ring. It gives no understanding of how the hydroxide atom affects the system because the oxygen atom is not within the ring.
The hydroxide will affect the electron distribution around the ring. This animation shows it nicely with resonance structures:
(source)
The resonance pictures make it easy to see, but it is important to keep in mind that molecules do not actually have resonance structures. A more accurate way of seeing it would be:
The $\ce{p}_z$of $\ce{O}$ is delocalized into $\pi^{*}$ of $\ce{C1}$, weakining $\ce{C1-C2}$ and $\ce{C1-C6}$ bonds, increasing the density on $\ce{C2}$ and $\ce{C6}$ by kicking the electrons in the bonding orbitals closer to them. The $\ce{p}_z$ electrons of $\ce{C2/C6}$ move into the $\pi^*$ of $\ce{C3/C5}$, which in turn results in an increased density on $\ce{C4}$.
This is still an MO simplification, and to get the accurate picture you would simply have to do the calculations.
It is still possible for an aromatic ring current to flow through the ring in the presence of a magnetic field, as we can see from NMR, but perhaps it feels more like a roller coaster now.