A B767-300 Captain reported conducting an autoland test which resulted in a centerline tracking deviation after touchdown.

Narrative

After reviewing the flight plan; I noted that a Flight Control Computer check was required. Although I have been very reluctant in the past to perform autoland checks with passengers on board due to the many variables which no one at this Company seems concerned with. Maintaining a sterile environment around runway or wind conditions which may be within limits but since most autoland approaches are to low visibility low wind conditions doing these during normal operations is dangerous and unsafe. Coming to the point; as we landed; after flying all night; the plane touched down in the middle of the runway then immediately deviated left of course; nearly ending a perfectly safe flight in disaster. Although I appreciate the companies continued effort to gloss over the inherent danger of testing our aircraft with passengers aboard; someone is going to end up in the grass or worse with lots of pointing fingers which will no doubt include the Captain who was just doing another autoland check to save the company money.