No. Calibrating autofocus has nothing to do with manual focus. This is because the light used for autofocus does not follow the same optical path as the the light used for manual focus.
The mirrors of cameras with Phase Detection Autofocus (PDAF) have a mirror that is only semi-reflective in the center. Some of the light is reflected up to the viewscreen. Some of the light passes through the mirror and is reflected down into the AF array by a secondary mirror located behind the main mirror.
When you use manual focus, you focus based upon what you see in the viewfinder which is the image formed on the viewscreen at the top of the camera's light box. If manually focusing to the sharpest focus distance as seen through the viewfinder results in back or front focussed photos, then the position of the viewscreen needs to be adjusted.
AFMA or AF Fine Tune does not do anything to the physical position of anything in the camera. Rather, it is a software adjustment that affects the instructions the camera sends to the lens with regard to the requested position of the lens' focus mechanism.
Keep in mind that AFMA and AF Fine Tune only affect PDAF - that is, focusing done with the mirror down. When using contrast detection AF (CDAF) in Live View, the image sensor is used for both focusing and taking the picture. Since the image sensor doesn't move between focusing and capturing the image, the focus distance needs no calibration. Note than even when in Live View, some cameras have options to do PDAF by dropping the mirror long enough to AF with the PDAF system rather than by using the image sensor based CDAF.