  In this paper we address the question of whether high-temperature
superconductors have anything in common with BCS-BEC crossover theory. Towards
this goal, we present a proposal and related predictions which provide a
concrete test for the applicability of this theoretical framework. These
predictions characterize the behavior of the Ginzburg-Landau coherence length,
$\xi_0^{\text{coh}}$, near the transition temperature $T_{\text{c}}$, and
across the entire superconducting $T_{\text{c}}$ dome in the phase diagram.
That we are lacking a systematic characterization of $\xi_0^{\text{coh}}$ in
the entire class of cuprate superconductors is perhaps surprising, as it is one
of the most fundamental properties of any superconductor. This paper is written
to motivate further experiments and, thus, address this shortcoming. Here we
show how measurements of $\xi_0^{\text{coh}}$ contain direct indications for
whether or not the cuprates are associated with BCS-BEC crossover and, if so,
where within the crossover spectrum a particular superconductor lies.
