We conducted 22 GHz 1 '' Jansky Very Large Array imaging of 100 radio-quiet X-ray-selected active galactic nuclei (AGN) from the Swift-Burst Array Telescope (Swift-BAT) survey. We find AGN-driven kiloparsec-scale radio structures inconsistent with pure star formation in 11 AGN. The host galaxies of these AGN lie significantly below the star-forming main sequence, indicating suppressed star formation. While these radio structures tend to be physically small compared to the host galaxy, the global star formation rate of the host is affected. We evaluate the energetics of the radio structures interpreted first as immature radio jets, and then as consequences of an AGN-driven radiative outflow, and compare them to two criteria for successful feedback: the ability to remove the CO-derived molecular gas mass from the galaxy gravitational potential and the kinetic energy transfer to molecular clouds leading to v(cloud) > sigma(*). In most cases, the jet interpretation is insufficient to provide the energy necessary to cause the star formation suppression. Conversely, the wind interpretation provides ample energy in all but one case. We conclude that it is more likely that the observed suppression of star formation in the global host galaxy is due to interstellar medium interactions of a radiative outflow, rather than a small-scale radio jet.