  With the remarkable increase in scale and precision provided by upcoming
galaxy redshift surveys, systematic errors that were previously negligible may
become significant. In this paper, we explore the potential impact of
low-magnitude systematic redshift offsets on measurements of the Baryon
Acoustic Oscillation (BAO) feature, and the cosmological constraints recovered
from such measurements. Using 500 mock galaxy redshift surveys as our baseline
sample, we inject a series of systematic redshift biases (ranging from +/-0.2%
to +/-2%), and measure the resulting shift in the recovered isotropic BAO
scale. When BAO measurements are combined with CMB constraints (in both
{\Lambda}CDM and wCDM cosmologies), plausible systematics introduce a
negligible offset on combined fits of H0 and {\Omega}m, and systematics must be
an order of magnitude greater than this plausible baseline to introduce a
1-{\sigma} shift on such combined fits. We conclude that systematic redshift
biases are very unlikely to bias constraints on parameters such as H0 provided
by BAO cosmology, either now or in the near future. We also detail a
theoretical model that predicts the impact of uniform redshift systematics on
{\alpha}, and show this model is in close alignment with the results of our
mock survey analysis.
