The application of imaging techniques based on ensembles of nitrogen-vacancy (NV) sensors in diamond to characterize electrical devices has been proposed, but the compatibility of NV sensing with operational gated devices remains largely unexplored. Here we report the fabrication of graphene field-effect transistors directly on the diamond surface and their characterization by NV microscopy. The current density within the gated graphene is reconstructed from NV-magnetometry measurements under both mostly p– and n-type doping, but the exact doping level is found to be affected by the measurements. Additionally, we observe a surprisingly large modulation of the electric field at the diamond surface under an applied gate potential, seen in NV-photoluminescence and NV-electrometry measurements, suggesting a complex electrostatic response of the oxide-graphene-diamond structure. Possible solutions to mitigate these effects are discussed.