Monolayer hBN has attracted interest as a potentially weakly interacting 2D insulating layer in heterostructures. Recently, wafer-scale hBN growth on Cu(111) has been demonstrated for semiconductor chip fabrication processes and transistor action. For all these applications, the perturbation on the underlying electronically active layers is critical. For example, while hBN on Cu(111) has been shown to preserve the Cu(111) surface state 2D electron gas, it was previously unknown how this varies over the sample and how it is affected by local electronic corrugation. Here, we demonstrate that the Cu(111) surface state under wafer-scale hBN is robustly homogeneous in energy and spectral weight over nanometer length scales and over atomic terraces. We contrast this with a benchmark spectral feature associated with interaction between BN atoms and the Cu surface, which varies with the Moire pattern of the hBN/Cu(111) sample and is dependent on atomic registry. This work demonstrates that fragile 2D electron systems and interface states are largely unperturbed by local variations created by the hBN due to atomic-scale interactions with the substrate, thus providing a remarkably transparent window on low-energy electronic structure below the hBN monolayer.