Active galactic nuclei (AGN) are considered possible sites of hadronic particle acceleration and are, therefore, promising neutrino source candidates. The IceCube Collaboration recently reported an excess of neutrino events in the 1.5 - 15 TeV range associated with the nearby Seyfert II galaxy NGC 1068, which hosts an intrinsically luminous AGN that is heavily obscured by gas and dust. Due to the lack of observable gamma-rays in this energy range, it seems that these neutrinos are most likely produced in photohadronic interactions in the vicinity of the central black hole. Motivated by this result, we explore the prospects of observing other hidden neutrino sources with similar neutrino production mechanisms. For this purpose, we use Monte Carlo simulations based on multi-wavelength observations of this class of sources. Applying approximate methods for point source searches combined with publicly available detector information, we then make predictions about the detectability of the resulting neutrino emission with IceCube and planned next-generation detectors, such as IceCube-Gen2 and KM3NeT. Connecting our findings on the diffuse flux from the source population as a whole to the possibility of detecting nearby individual neutrino sources allows us to draw a coherent picture of the contribution of these sources to astrophysical neutrino observations.