We compare the magnetic field orientation for the young giant molecular cloud Vela C inferred from 500 μm polarization maps made with the BLASTPol balloon-borne polarimeter to the orientation of structures in the integrated line emission maps from Mopra observations. Averaging over the entire cloud we find that elongated structures in integrated line-intensity or zeroth-moment maps, for low-density tracers such as 12CO and 13CO J → 1 – 0, are statistically more likely to align parallel to the magnetic field, while intermediate- or high-density tracers show (on average) a tendency for alignment perpendicular to the magnetic field. This observation agrees with previous studies of the change in relative orientation with column density in Vela C, and supports a model where the magnetic field is strong enough to have influenced the formation of dense gas structures within Vela C. The transition from parallel to no preferred/perpendicular orientation appears to occur between the densities traced by 13CO and by C18O J → 1 – 0. Using RADEX radiative transfer models to estimate the characteristic number density traced by each molecular line, we find that the transition occurs at a molecular hydrogen number density of approximately 103 cm‑3. We also see that the Centre Ridge (the highest column density and most active star-forming region within Vela C) appears to have a transition at a lower number density, suggesting that this may depend on the evolutionary state of the cloud.