  Fully occupied or unoccupied bands in a solid are often considered inert and
irrelevant to a material's low-energy properties. But the discovery of enhanced
superconductivity in heavily electron-doped FeSe-derived superconductors poses
questions about the possible role of incipient bands (those laying close to but
not crossing the Fermi level) in pairing. To answer this question, researchers
have studied pairing correlations in the bilayer Hubbard model, which has an
incipient band for large interlayer hopping $t_\perp$, using many-body
perturbation theory and variational methods. They have generally found that
superconductivity is enhanced as one of the bands approaches the Liftshiz
transition and even when it becomes incipient. Here, we address this question
using the nonperturbative quantum Monte Carlo (QMC) dynamical cluster
approximation (DCA) to study the bilayer Hubbard model's pairing correlations.
We find that the model has robust $s_\pm$ pairing correlations in the large
$t_\perp$ limit, which can become stronger as one band is made incipient. While
this behavior is linked to changes in the effective interaction, we further
find that it is counteracted by a suppression of the intrinsic pair-field
susceptibility and does not translate to an increased $T_c$. Our results
demonstrate that the highest achievable transition temperatures in the bilayer
Hubbard model occur when the system has two bands crossing the Fermi level.
