  Chains and arrays of phosphorus donors in silicon have recently been used to
demonstrate dopant-based quantum simulators. The dopant disorder present in
fabricated devices must be accounted for. Here, we theoretically study
transport through disordered donor-based $3\times 3$ arrays that model recent
experimental results. We employ a theory that combines the exact
diagonalization of an extended Hubbard model of the array with a
non-equilibrium Green's function formalism to model transport in interacting
systems. We show that current flow through the array and features of measured
stability diagrams are highly resilient to disorder. We interpret this as an
emergence of uncomplicated behavior in the multi-electron system dominated by
strong correlations, regardless of array filling, where the current follows the
shortest paths between source and drain sites that avoid possible obstacles.
The reference $3\times 3$ array has transport properties very similar to three
parallel 3-site chains coupled only by interchain Coulomb interaction, which
indicates a challenge in characterizing such devices.
