You could always create a hatch in paperspace with ANSI31 or something, in grey. Or if "paperspace plots last" is set, maybe the hatch would be -behind- the objects, and as such you could use a solid or densely-dotted hatch to create the visual difference, and shade the white-space instead of shading the linework?
Otherwise, I'm with El Jefe, my first impression is that I'd have to create a rectangular-donut viewport (since you can do a vpclip or create a vport from a closed polyline**), override the layer color of everything to something grey on the color table, then have a donut-hole-rectangle viewport for the regular view with no overrides.
** You might have to create the viewport not as a true donut, but more like the outlines of your thumb and forefinger as they touch tips. Sort of the outline of the letter "U" if you bent the tops to meet.