For the 757/767, a "NO FLARE" annunciation is an automatic go-around. As has been mentioned, you will most likely touch down during the go-around, but the pitch up maneuver will insure a safe attitude at touchdown. Further, the power will be coming up, and there will be a positive climb almost immediately.
The real threat, if one should attempt a manual landing, is a bounced landing. The bounced landing recovery procedure would be problematic, to say the least. A go-around from the top of the bounce is probably not where you want to be, either. All things considered, a manual landing would be acceptable ONLY is the visual references were adequate for a flare and touchdown, which would be rather more than the visual references required for fail-passive CAT III minima. Probably wise to make this assessment a bit before the point at which you are expecting a FLARE annunciation. Otherwise, a simple flick of the thumb should do the trick.