In order to better understand how active galactic nuclei (AGN) effect the interstellar media of their host galaxies, we perform a meta-analysis of the CO emission for a sample of $z=0.01-4$ galaxies from the literature with existing CO detections and well-constrained AGN contributions to the infrared (67 galaxies). Using either Spitzer/IRS mid-IR spectroscopy or Spitzer+Herschel colors we determine the fraction of the infrared luminosity in each galaxy that can be attributed to heating by the AGN or stars. We calculate new average CO spectral line ratios (primarily from Carilli & Walter 2013) to uniformly scale the higher-$J$ CO detections to the ground state and accurately determine our samples molecular gas masses. We do not find significant differences in the gas depletion timescales/star formation efficiencies (SFEs) as a function of the mid-infrared AGN strength ($f_{rm AGN}({rm MIR})$ or $L_{rm IR} ({rm AGN})$), which indicates that the presence of an IR-bright AGN is not a sufficient sign-post of galaxy quenching. We also find that the dust-to-gas ratio is consistent for all sources, regardless of AGN emission, redshift, or $L_{rm IR}$, indicating that dust is likely a reliable tracer of gas mass for massive dusty galaxies (albeit with a large degree of scatter). Lastly, if we classify galaxies as either AGN or star formation dominated, we do not find a robust statistically significant difference between their CO excitation.
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