Just to clarify: On a 737 the A/P does NOT need any FD to operate, of course the AP can fly the plane without any FD's activated - what is regular practice by the way. But the two modes LNAV and VNAV do require the FD activated before AP activation is possible. AP is engagable only into basic modes like LVL CHG or HDG SEL if FD's are OFF. You just cannot select LNAV and VNAV on the MCP with FD's off.
For example: If i get a direct on a raw data departure later on, i fly manually "the magenta line", first FD on, then LNAV, then VNAV, if everything's fine and no corrections by the AP to be expected, i engage AP and grab a cup of coffee.
No idea how this works on a 757/767 though, but can hardly imagine there are differencies, at least with the cup of coffee.