The formation of a self-limited metallic bilayer is reported during the growth of GaN by plasma-assisted molecular beam epitaxy on graphene on (0001) SiC. Depending on growth conditions, this layer may consist of either Ga or In, which gets intercalated between graphene and the SiC surface. Diffusion of metal atoms is eased by steps at SiC surface and N plasma induced defects in the graphene layer. Energetically favorable wetting of the (0001) SiC surface by Ga or In is tentatively assigned to the breaking of covalent bonds between (0001) SiC surface and carbon buffer layer. As a consequence, graphene doping and local strain/doping fluctuations decrease. Furthermore, the presence of a metallic layer below GaN opens the way to the development of devices with a spontaneously formed metallic electrode on their back side.