optics - Are points off-center from the lens axis out of focus?

If I take a picture of a flat surface perpendicular to the direction of the lens (i.e. the surface is facing directly at the camera), and I focus on the center, are the points off center in perfect focus, since they are further from the lens than the center point?

Alternatively, do camera lenses have a way to account for this?

If in fact the points off center are slightly out of focus, couldn't this have a significant effect on achieving focus across the entire surface, especially if the camera were close to the object?

Thanks to anyone who can shed some light on this.