Linear time-distance helioseismic inversions are carried out using several filtering schemes to determine vector flow velocities within two ~1002 Mm2 × 20 Mm realistic magnetohydrodynamic sunspot simulations of 25 hr. One simulation domain contains a model of a full sunspot (i.e., one with both an umbra and penumbra), while the other contains a pore (i.e., a spot without a penumbra). The goal is to test current helioseismic methods using these state-of-the-art simulations of magnetic structures. We find that horizontal flow correlations between inversion and simulation flow maps are reasonably high (~0.5-0.8) in the upper 3 Mm at distances exceeding 25-30 Mm from spot center, but are substantially lower at smaller distances and larger depths. Inversions of forward-modeled travel times consistently outperform those of our measured travel times in terms of horizontal flow correlations, suggesting that our inability to recover flow structure near these active regions is largely due to the fact that we are unable to accurately measure travel times near strong magnetic features. In many cases the velocity amplitudes from the inversions underestimate those of the simulations by up to 50%, possibly indicating nonlinearity of the forward problem. In every case, we find that our inversions are unable to recover the vertical flow structure of the simulations at any depth.