Yes, very quickly -- even more quickly than with other approaches, because your eye saccades really fast. (Although you probably don't have to render intermediate frames during the saccade, because IIRC your brain sort of ignores incoming detail during the movement itself.)
The win is that you have to render a much smaller patch of high-resolution detail, which saves computation in some parts of the pipeline. You've still got to do all the intersection, bounding-pyramid, depth-sorting and whatnot for your whole model (I assume -- it's been close to thirty years since I've done much in 3D graphics), but you don't have to crank out as many pixels. To get "retina" resolution, you'd need a foveal patch no more than maybe 500 pixels in diameter, and the rest of the visual field could probably get by with another 500 pixels on a side. That's a lot less painting than the stack of 3840x2160 screens you'd need to fill the whole visual field at that resolution -- probably between one and two orders of magnitude smaller.
As far as the rest of the pipeline, I guess you win because those rapid saccades don't significantly change the viewpoint (head location), so there won't be a lot of changes to object order or occlusion. (Your pupil does shift its position, since the eye's center of rotation is obviously near the center of the eyeball, but any virtual object that close to your eye ought to be blurred anyhow, unless you're playing the final levels of Quest for Nearsightedness.)