Would a seat post mounted back rack act like a rear fender?
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.