  On both observational and theoretical grounds, the disk of our Galaxy should
be accreting cool gas with temperature ~<10^5 K via the halo at a rate ~1
M_sun/yr. At least some of this accretion is mediated by high velocity clouds
(HVCs), observed to be traveling in the halo with velocities of a few 100 km/s
and occasionally impacting the disk at such velocities, especially in the outer
regions of the Galaxy. We address the possibility of particle acceleration in
shocks triggered by such HVC accretion events, and the detectability of
consequent non-thermal emission in the radio to gamma-ray bands and high-energy
neutrinos. For plausible shock velocities ~300 km/s and magnetic field
strengths ~0.3-10 muG, electrons and protons may be accelerated up to ~1-10 TeV
and ~30-10^3 TeV, respectively, in sufficiently strong adiabatic shocks during
their lifetime of ~10^6 yr. The resultant pion decay and inverse Compton
gamma-rays may be the origin of some unidentified Galactic GeV-TeV sources,
particularly the "dark" source HESS J1503-582 that is spatially coincident with
anomalous HI structure known as "forbidden-velocity wings". Correlation of
their locations with star-forming regions may be weak, absent or even opposite.
Non-thermal radio and X-ray emission from primary and/or secondary electrons
may be detectable with deeper observations. The contribution of HVC accretion
to Galactic cosmic rays is subdominant, but could be non-negligible in the
outer Galaxy. As the thermal emission induced by HVC accretion is likely
difficult to detect, observations of such phenomena may offer a unique
perspective on probing gas accretion onto the Milky Way and other galaxies.
