I spoke to an Engineer at Equalizer and he confirmed that WDH's do increase your hitch weight.

Receiver hitches have two ratings. The ratings of receiver hitch on the tow vehicle are important to safe towing, so you'll want to be sure what the receiver on your truck can handle. Receiver hitches are rated for their Load-Bearing and Weight-Distributing capacities. Typically receivers display one of the two, if not both ratings. If only one is shown, it is important to find out which rating it represents. If it is the
load-bearing maximum, that means that your receiver will also have a weight-distributing maximum, and you will want to find that out to make sure that the trailer you're towing doesn't exceed the weight distributing maximum rating. If that's your weight-distributing maximum, you will have to tow trailers with less than that rating in the loaded tongue weight, unless you upgrade the receiver on your tow vehicle.

Using a weight distribution hitch, will allow you to use the heavier "Weight Distribution" or "Weight Distributing" ratings instead of the "Load Bearing" rating.