gauge theory - Does spontanous symmetry breaking affect Noethers theorem?

Does spontanous symmetry breaking affect the existence of a conserved charge?

And how does depend on whether we look at a classical or a quantum field theory (e.g. the weak interacting theory)?

(In the quantum case, if we don't want to speak of the Noether theorem, the question can be worded as how does the field breaking the symmetry affect the identities resulting from the Lagrangian symmetry.)

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The question came up as I wondered if you can make a gauge theory out of every "kernel" of the process in which you compute obervables. In the sense that if

$$\langle A \rangle_\psi=\int (\psi^*A\psi)\text d V,$$

the transformation $T:\phi\rightarrow \text e^{i\alpha}\phi$ is in the kernel of $\langle - \rangle_\psi$.