operators - Background fields in canonical formalism

In quantum electrodynamics problems involving background fields, most text books usually makes the following substitution

$$A^\mu \rightarrow A^{'\mu}= A_0^{\mu}+A_{c}^{\mu}$$

Where $A_{c}$ is classical field satisfying Maxwell equations.

In the path integral formalism this seems reasonable to do since, $A_0^{\mu}$ and $A_{c}^{\mu}$ are $c$ numbers but in the canonical formalism $A_0^{\mu}$ are an operator and $A_{c}^{\mu}$ a $c$ number.

Is this a reasonable thing to do?