From you description of your intent, that's completely a waste.

First, let me tell you what a weight distributing hitch really is. It's not the hitch (i.e., the receiver and support to the car's frame), per se. It's actually a specially designed insert (the part that you put into the 2" square receiver), with springs (actually, long metal arms that lie parallel to but below the height of the trailer's tongue) that link via chains to the trailer's tongue.

First, you have to think of the connection between the trailer's coupler (to which the hitch ball attaches) and the hitch receiver's insert (to which the ball attaches) as two "backbones" that can flex at the ball-coupler joint.
Normally, your hitch up your trailer so that the trailer's tongue and frame are horizontal (your receiver insert should have the right lift or drop so that the height of the ball allows this) -- although this isn't necessary in your case because you're not taking the trailer on the road. The trailer's tongue weight is supported solely by the rear suspension, obviously, and it will sag a bit.

However, with the weight distributing hitch, all four wheels of your car support the weight of the trailer. How this happens is that, when you hook up the trailer, you have to tighten those aforementioned chains, so they actually force the trailer tongue's ball receiver (and the car's rear) upwards, and when you have the right tension on the chains (so that the tongue is horizontal), some of the trailer tongue's weight is actually pushing down on the front of the vehicle as well as the rear -- hence the name, weight distributing hitch, because it distributes the trailer's tongue weight to the front as well as the rear of the vehicle.