She's just really sleepy (due to low blood pressure apparently) so her falling asleep like this isn't too surprising. Although in this case, I'm imagining that Mako just pretended to fall asleep while flirting with Saori in order to try and get Saori to take the lead for once.
That’s true and I agree, but they do belong in the same class of battleships. That’s essentially being in the same family so Shipcest seems more fitting :p