The boron nitride nanomesh is a corrugated monolayer of hexagonal boron nitride (h--BN) on Rh(111), which so far has been studied mostly under ultrahigh vacuum conditions. Here, we investigate how copper underpotential deposition (upd) can be used to quantify defects in the boron nitride monolayer and to assess the potential window of the nanomesh, which is important to explore its functionality under ambient and electrochemical conditions. In dilute sulfuric acid, the potential window of h--BN/Rh(111) is close to 1 volt, i.e. larger than that of the Rh substrate, and is limited by molecular hydrogen evolution on the negative and by oxidative removal on the positive side. From copper upd on pristine h--BN/Rh(111) wafer samples, we estimate a collective defect fraction on the order of 0.08-0.7% of the geometric area, which may arise from line and point defects in the h--BN layer that are created during its chemical vapour deposition. Overpotential deposition (opd) is demonstrated to have significant consequences on the defect area. We hypothesise that this non--innocent Cu electrodeposition involves intercalation originating at initial defects, causing irreversible delamination of the h--BN layer; this effect may be used for 2D material nanoengineering. On the relevant timescale, upd itself does not alter the defect area on repeated cycling; therefore, metal upd may find use as a general tool to determine the collective defect area in hybrids between 2D materials and various substrate metals.