Will the ship's physical profile actually affect atmospheric flight? If we did this maneuver in the Herald, would we fall to the ground faster than we would in the Gladius?

Absolutely. We do simulate what are called lifting bodies, so surfaces that have the sort of geometry to support lift but are not necessarily wings can generate some lift, but not very much. And you will feel that difference. So the Gladius can obviously glide a lot further than something like the Aurora.