In the paper Cooper pair tunnelling into a Quantum Hall fluid, the author models a superconductor in tunnelling contact with a Quantum Hall fluid. The superconductor is modelled
... in terms of a bosonic pair field, $\hat c$ , which exhibits long-ranged (vortex-glass) order and has a non-zero condensate, $\langle \hat c \rangle = \Delta $.
The author gives a tunnelling Hamiltonian
$$H = t [\hat\psi_{\uparrow}(x=0)^\dagger \hat\psi_{\uparrow}(x=\xi)^\dagger \hat c(x=0) + H.c.]$$
and argues that
Since the superconductor has a non-zero condensate, it is legitimate to simply replace the operator $\hat c$ in [the Cooper pair tunnelling Hamiltonian] by the c-number $\Delta$.
As I understand it, $\hat c = \hat\eta_{\uparrow}(x) \hat\eta_{\downarrow}(x^\prime)$, where $\hat \eta_\sigma (x)$ is the electron operator. According to BCS theory,
$$\langle \hat\eta_{\uparrow}(x) \hat\eta_{\downarrow}(x^\prime) \rangle = \Delta,$$
but what is unclear to me is under what circumstances is it OK to just replace the pair operator with its expectation value? What does the author mean by "it is legitimate"? Is it some kind of mean field approximation?