  In accretion-based models for Sgr A* the X-ray, infrared, and millimeter
emission arise in a hot, geometrically thick accretion flow close to the black
hole. The spectrum and size of the source depend on the black hole mass
accretion rate $\dot{M}$. Since Gillessen et al. have recently discovered a
cloud moving toward Sgr A* that will arrive in summer 2013, $\dot{M}$ may
increase from its present value $\dot{M}_0$. We therefore reconsider the
"best-bet" accretion model of Moscibrodzka et al., which is based on a general
relativistic MHD flow model and fully relativistic radiative transfer, for a
range of $\dot{M}$. We find that for modest increases in $\dot{M}$ the
characteristic ring of emission due to the photon orbit becomes brighter, more
extended, and easier to detect by the planned Event Horizon Telescope submm
VLBI experiment. If $\dot{M} \gtrsim 8 \dot{M}_0$ this "silhouette of the black
hole will be hidden beneath the synchrotron photosphere at 230 GHz, and for
$\dot{M} \gtrsim 16 \dot{M}_0$ the silhouette is hidden at 345 GHz. We also
find that for $\dot{M} > 2 \dot{M}_0$ the near-horizon accretion flow becomes a
persistent X-ray and mid-infrared source, and in the near-infrared Sgr A* will
acquire a persistent component that is brighter than currently observed flares.
