It is true that the body shape won't have any effect on the way microphones are picking the sound.
However, the strings (which are vibrating) are attached to the body. Part of the string vibration will be transferred to the body and, obviously part of the vibration of the body will be transferred to the strings.
This way, the shape of the body can actually have an influence on the sound produced by the strings: if some frequencies are favored or not, depending, for instance, if the body will "resonate" well at these frequencies. The exact way it will influence the strings or vibrates is, I think, a very difficult question though. But it is clear that the strings are not attached to an "unmovable" frame like we like them to be attached in Physics…
Obviously, this is a secondary effect, but as the system body+strings is quite coupled, you can imagine the former has an effect on the behavior of the later.