  We consider some general implications of bright gamma-ray counterparts to
fast radio bursts (FRBs). We show that even if these manifest in only a
fraction of FRBs, gamma-ray detections with current satellites (including
Swift) can provide stringent constraints on cosmological FRB models. If the
energy is drawn from the magnetic energy of a compact object such as a
magnetized neutron star, the sources should be nearby and be very rare. If the
intergalactic medium is responsible for the observed dispersion measure, the
required gamma-ray energy is comparable to that of the early afterglow or
extended emission of short gamma-ray bursts. While this can be reconciled with
the rotation energy of compact objects, as expected in many merger scenarios,
the prompt outflow that yields the gamma-rays is too dense for radio waves to
escape. Highly relativistic winds launched in a precursor phase, and forming a
wind bubble, may avoid the scattering and absorption limits and could yield FRB
emission. Largely independent of source models, we show that detectable radio
afterglow emission from gamma-ray bright FRBs can reasonably be anticipated.
Gravitational wave searches can also be expected to provide useful tests.
