We present a thorough numerical study of the Richardson model with quenched disorder (a fully-connected XX-model with longitudinal random fields). We find a relation between the inverse participation ratio, the Edwards-Anderson order parameter and the average Hamming distance between spin configurations covered by a typical eigenstate for which we conjecture a remarkably simple form for the thermodynamic limit. We find a sudden onset of an exponentially large IPR on the space of spin configurations, although local observables (single-spin expectation values) never achieve thermalization. We also studied the random process defined by the spread of a typical eigenstate on configuration space, highlighting several similarities with hopping on percolated hypercube, a process used to mimic the slow relaxation of spin glasses.