Would a seat post mounted back rack act like a rear fender? Specifically I want to know if the right one would stop the rider's back from getting splattered with rain. That way it does double duty as a fender and a rack.I want a light duty back rack for day to day cargo. If I am getting bulky groceries or doing the laundry I can always use a backpack.
I like the minimalist lines of some of the ones I have seen. They suit my bike.
I'd say it depends on the length of the rack you're going to attach.

It's all about the physics - the water droplets, when they detach from the tyre they move perpendicular to the perimeter of the wheel. If the rack is long enough, the droplets that might reach your back are hitting the rack (acting as a mudguard). 

The ideal situation would be when the rack reaches to the furthest rear point of the wheel. Then only the droplets travelling vertically are not covered by the rack.

However when the rack gets shorter, the more droplets travel to the front, thus direction of your back.

Short story long - have a look at the picture:


black is the bicycle (obvious)
red is the rack
blue is the  most front-travelling droplet that might hit your back



I hope you get the idea.