Yes, the image will normally be distorted, in that objects close to the lens will look larger and those farther away appear to be smaller.

For the human face viewed straight on, this is not at all flattering, as the nose will look (a tiny bit) larger than it should, the eyes and mouth smaller, and the ears and head even smaller (in relation to a 50mm view on any full-frame camera like the Sony A7 you mention, or in comparison to how we view the world around us with our visual sense (eyes and brain)). Since we pay attention to a speaker's eyes and the mouth, it would seem to add a risk of distractingthe viewer from the words, or looking odd or unattactive.

Depending on how close you get to the subject, in addition to the distortion, a shallow depth of field might mean parts of the face might end up 'soft' or blurred, and it may be that these would look better sharp.

Keep in mind that the not-in-focus elements are likely to look different depending on focal length - the 70mm or even 50mm length could be used in a set-up to produce a 'look' of subject versus background that might be what you are aiming for.

Here's an interesting discussion of achieving a shallow depth of field look with mid-range apertures. In the end, as a photograph or video is (primarily) visual, it seems like trying out the camera and lens combination is going to be the best way to work out how the distortion affects the image and whether your focal length will reach your aims!