I've never tried autolanding on one AP, so just a guess: my bet is Boeing, in it's typical legal telegraphic wording, could not make any reference to such a sensitive issue like autoland on only one AP.
But actually the real thing is just capable of doing it, although not certified thus not documented.
This is true on other airplanes also, like the Dornier 328, which will "autoland" if you leave the AP engaged till touchdown.
Of course, this was observed in the sim, so we can't be sure 100%.
Only way to be sure is trying on the airplane, with no pax, of course; if you see no flare by 30 ft, still time to disengage and pull.
Any volunteer?