  Velocity dispersion measurements of recently discovered Milky Way satellites
with $M_V\gtrsim-7$ imply they posses high mass-to-light ratios. The expected
velocity dispersions due to their baryonic mass are $\sim0.2$\,km\,s$^{-1}$,
but values $\gtrsim3$\,km\,s$^{-1}$ are measured. We perform Monte Carlo
simulations of mock radial velocity measurements of these systems assuming they
have mass-to-light ratios similar to globular clusters and posses an
unidentified binary star population, to determine if these stars could boost
the velocity dispersion to the observed values. We find that this hypothesis is
unlikely to produce dispersions much in excess of $\sim 4.5$\,km\,s$^{-1}$, in
agreement with previous work. However, for the systems with potentially the
smallest velocity dispersions, values consistent with observations are produced
in 5-40% of our simulations for binary fractions in excess of
$f_{bin}(P\le10$\,yrs$)\sim5%$. This sample includes the dwarf galaxy
candidates that lie closest to classical globular clusters in $M_V-r_h$ space.
Considered as a population, it is unlikely that all of these dwarf galaxy
candidates have mass-to-light ratios typical of globular clusters, but boosting
of the observed dispersion by binaries from near-zero values cannot be ruled
out at high confidence for several individual dwarf galaxy candidates. Given
the importance of obtaining accurate velocity dispersions and dynamical masses
for the faintest satellites, it is clearly desirable to exclude directly the
possible effect of binaries on these systems. This requires multi-epoch radial
velocity measurements with individual uncertainties of
$\lesssim$1\,km\,s$^{-1}$ to identify spectroscopic binaries with orbital
velocities of order the observed velocity dispersion.
