Different types of rotating disk boundary layers were previously shown to be absolutely unstable. The present study checks if this is also true for the flow between narrowly spaced co-rotating disks with merged boundary layers and imposed throughflow. The described method is able to reproduce the absolute instability of the von Kármán boundary layer and of radially outward flow between co-rotating disks with separated boundary layers. Nevertheless, no absolute instability is found for the case of narrow disk spacing with merged boundary layers for both radially inward and outward flow. The data does however show convective instability. Stability maps are provided for the analyzed parameter space.