I know with my stock suspension and carrying around that weight in the back seats/trunk.. The rear would sag super low, tucking a little bit. Haven't put any weight in the rear yet with my new setup so I don't know.
I'd imagine the coilovers would probably be stiffer and could support the weight difference without the sag. I would also guess that the Koni setup is a much better DD ride depending on which springs are used. All depends on which coilovers you are thinking of though.