Metalcutter,
A drill sharpened with one lip longer than the other must cut off center whether started on the surface, in a spot drill cone, or following a pilot drill. In the case of the surface start, the point will trace a circle on the part until it is forced in to the work at some point on that circle, after which it will drill both off center and oversize. In either the pilot drill case or the spot drill cone, pressure on the unequal lips will force the drill to bend so that the lips center the point on the hole or spot drill cone, after which the drill will cut on location but oversize.
I recently discussed the effect of a new but incorrectly sharpened drill on following a pilot hole on this thread. My pride is still smarting.
http://www.practicalmachinist.com/vb/showthread.php?t=159488