No, face crop won’t cut out the images.
The batch mode for cutouts is for images tat are already extracted with transparency. There are different options available for cutouts vs. non-cutouts. When running a batch for cutouts you won’t have the option to save as jpg because jpg doesn’t support transparency and the images would get flattened when saving. Also, the option for content aware gap fill isn’t available when running cutouts because you don’t want to fill the transparency.