Hey Fuct
No, the nismos don't have a different fuel pump from the other Zs. Yes, running low on fuel will cause the pump to heat/work harder. Nissan fuel pump (17040-1EK0B) is a revised pump that doesn't come on '12 or older models. I'm not for sure if 2013s have it.
Now I request you take a sweeping right hander on very low fuel w/that revised fuel pump (17040-1EK0B) and see if it still fuel starves. Obviously take a small gas can w/you or have a friend trail behind you w/it so you don't have to call a tow. Please let the Z community know the findings. Thank you.