A point-like source of TeV gamma-rays has recently been seen towards the Galactic center by HESS and other air Cerenkov telescopes. In recent work (Ballantyne et al. 2007), we demonstrated that these gamma-rays can be attributed to high-energy protons that (i) are accelerated close to the event horizon of the central black hole, Sgr A*, (ii) diffuse out to pc scales, and (iii) finally interact to produce gamma-rays. The same hadronic collision processes will necessarily lead to the creation of electrons and positrons. Here we calculate the synchrotron emissivity of these secondary leptons in the same magnetic field configuration through which the initiating protons have been propagated in our model. We compare this emission with the observed GHz radio spectrum of the inner few pc region which we have assembled from archival data and new measurements we have made with the Australia Telescope Compact Array. We find that our model predicts secondary synchrotron emission with a steep slope consistent with the observations but with an overall normalization that is too large by a factor of 2. If we further constrain our theoretical gamma-ray curve to obey the implicit EGRET upper limit on emission from this region we predict radio emission that is consistent with observations, i.e., the hadronic model of gamma ray emission can, simultaneously and without fine-tuning, also explain essentially all the diffuse radio emission detected from the inner few pc of the Galaxy.