The problem is little clearer now.
Yes, it will increase the likelihood of fatigue as the situation you describe will severely overload on side of the threads. The seating surface, whether a shoulder or fastener head, should be perpendicular to the centerline of the threaded hole. As your are probably dealing with fine threads this will make this situation worse.
This is somewhat like a standard test to check the head and fillet on a fasteners.
If you could come back with a little more information such as the thread description and material and where you are experiencing failures on the fasteners you could get a better answer.