Actually, it is quite possible to suck air in a vertical dive with low fuel, I've done it a few times. However, you usually run out of altitude before you run out of fuel, because it does take a few moments for all the fuel in the line to empty and for the engine to die. At low throttle, it's even longer.

A 6-7 second dive? You've timed it? That's a LOOOOOOOONG time, you must be nearly a dot when you start the dive. I suspect your dives are a lot shorter than that.

Fuel will go to the back of the tank as the plane accelerates downwards, but you can reach terminal velocity. At that point, gravity + engine thrust = drag, and veloticy becomes constant, and all your fuel goes to the front of the tank. Getting to terminal velocity is a bit of a trick though, as, like I said above, you usually run out of altitude first. Though I think it's easier in a spin, as you reach terminal velocity faster. However the spinning motion also pushes the fuel and clunk around a bit, and might or might keep it from happening.

So, unless you are trying to make it happen, it almost never does.