Motivated by theoretical expectations that Nuclear Star Clusters (NSCs) in galactic centers may provide a favorable environment for super-massive black holes to form and/or efficiently grow, we set out to measure the fraction of nearby nucleated galaxies that also host an Active Galactic Nucleus (AGN). We targeted a distance-limited sample of 98 objects with the Chandra X-ray Telescope, down to a uniform X-ray luminosity threshold of $sim$10$^{38}$ erg s$^{-1}$. The sample is composed of 47 late-types and 51 early-types, enabling us to further investigate the active fraction as a function of galactic morphology. After correcting for contamination to the nuclear X-ray signal from bright X-ray binaries, we measure an active fraction $f$=11.2$%^{+7.4}_{-4.9}$ (1$sigma$ C.L.) across the whole sample, in agreement with previous estimates based on an heterogeneous combination of optical, X-ray and radio diagnostics, by Seth et al. (2008). After accounting for the different stellar mass distributions in our samples, we find no statistically significant difference in the active fraction of early- vs. late-type nucleated galaxies, with $f$=10.6$%^{+11.9}_{-4.9}$ and 10.8$%^{+11.3}_{-6.3}$, respectively. For the early-type nucleated galaxies, we are able to carry out a controlled comparison with a parent sample of non-nucleated galaxies covering the same stellar mass range, finding again no statistically significant difference in the active fraction. Taken at face value, our findings suggest that the presence of a NSC does not facilitate nor enhance accretion-powered emission from a nuclear super-massive black hole. This is true even for late-type nucleated galaxies, home to bluer NSCs and arguably larger gas reservoirs.
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