Because I've done this before, I had the files on hand

.
In practice, putting an image (here, the same torture test) as the cover image in a book will effectively yield that grayscale, ordered dithered thing you see in the second attachment.
I *can* capture those, because it's an H2O with zero hardware/kernel support for dithering.
Results would be different on my Forma

.
Fun fact that I don't remember if I'd ever tested before: if I drop the original PNG, and open that, it's displayed entirely unprocessed (again, because H2O).
EDIT: Huh, my full-quality JPEG encode apparently doesn't agree with vB, so I attached the source PNG as a third image, as well as the test ePub. Which I'm pretty sure I originally got from @jackie_w (as well as the original idea to use a double shiny pink gradient pattern for those tests

).
EDITē: Added the result in sleep mode (with said thumbnail generated by Nickel), to show that there's another process pass involved (or two if you don't use Calibre's Send To Device).
You'll probably have to look at the histogram to truly make the difference pop

.
Code:
ePub:
Colors: 8
Histogram:
11455: (0,0,0,65535) #000000FF black
73325: (9252,9252,9252,65535) #242424FF grey14
285218: (18761,18761,18761,65535) #494949FF srgba(73,73,73,1)
206692: (28013,28013,28013,65535) #6D6D6DFF srgba(109,109,109,1)
134613: (37522,37522,37522,65535) #929292FF srgba(146,146,146,1)
175086: (46774,46774,46774,65535) #B6B6B6FF srgba(182,182,182,1)
210374: (56283,56283,56283,65535) #DBDBDBFF grey86
446557: (65535,65535,65535,65535) #FFFFFFFF white
Sleep:
Colors: 256