Anne Sofie Tegner Anker, Jennifer L. Doleac, and Rasmus Landersø tell us yes:
This paper studies the effects of adding criminal offenders to a DNA database. Using a large expansion of Denmark’s DNA database, we find that DNA registration reduces recidivism within the following year by as much as 43% and it also increases the probability that offenders are identified. We thereby estimate the elasticity of crime with respect to the detection probability to be -2.7, implying that a 1% higher detection probability reduces crime by more than 2%. We also find that DNA registration makes offenders more likely to find employment, enroll in education, and live in a more stable family environment.
Via Ilya Novak (and others).