The recent detection of a gamma -ray flux from the direction of the Galactic center by EGRET on the Compton GRO raises the question of whether this is a point source (possibly coincident with the massive black hole candidate Sgr A*) or a diffuse emitter. Using the latest experimental particle physics data and theoretical models, we examine in detail the gamma -ray spectrum produced by synchrotron, inverse Compton scattering and mesonic decay resulting from the interaction of relativistic protons with hydrogen accreting onto a point-like object. Such a distribution of high-energy baryons may be expected to form within an accretion shock as the inflowing gas becomes supersonic. This scenario is motivated by hydrodynamic studies of Bondi-Hoyle accretion onto Sgr A*, which indicate that many of its radiative characteristics may ultimately be associated with energy liberated as this plasma descends down into the deep potential well. Earlier attempts at analyzing this process concluded that the EGRET data are inconsistent with a massive point-like object. Here, we demonstrate that a more careful treatment of the physics of p-p scattering suggests that a ~ 10^6 M_o black hole may be contributing to this high-energy emission.