Not true greys, no. You could certainly make an image that included the 256 real greys alongside another 256 shades in which the color values for RGB are not exactly the same. (IE, in addition to using #000000 through #FFFFFF you could add some arbitrary stripes where you subtract 1 from one of the RGB channels, IE, #FEFFFF.) But by definition those extra "greys" will actually be subtly "sepia toned". WHICH IS CHEATING.
They do sell video cards and monitors capable of 30 bit color now, so if you really want 1024 true greys you can have it. A setup to do it will run you around three grand. I have to admit I'm sort of curious if a double-blind test between one of those systems and an "equally high quality" IPS panel+24 bit card would really show that humans can tell the difference between 16 million and one billion colors.
The misleading part is the resolution of the CLUT doesn't necessarily tell you the resolution of the DACs. ***Using a CLUT for 15 bit color is actually unusual... (*** EDIT: Rest of this thought deleted. Glancing again at the piece of the manual I quoted I see the CLUT in this Powerbook doesn't do 15 bit indexed color, its palette register is 8 bits long. Derp. In my defence, the verbage of the service manual is nonstandard, since it says "CLUT" to refer to what in a VGA card would be the entire "RAMDAC", of which the CLUT is only a part, aka, the palette register. Anyway...) All PC "highcolor" VGA cards that did 15 or 16 bit color, aka, "Thousands of colors" in Mac terminology, still had *at least* six bit ADCs in their RAMDACs, they just couldn't use the entire range when in the highcolor mode. (Which leads to the odd situation that you could actually have more true grays running in an 8 bit grayscale mode than you could in "thousands of colors" mode, because, as you note, the effective grayscale resolution is only 5 bit in "thousands of colors" but it's six or 8 bit in the indexed mode.)
But, again, DAC only applies to the external monitor port on a Powerbook. Given the evidence I'd wager that the color LCD in the 540c could do 16 "real genuine according to Hoyle" greys, but when you have it set for grayscale it just might use dithering to fake a higher number. IF someone has the part number for the greyscale LCD they should Google it and see if they can find a datasheet. It's worth a shot.