DME does work for carbing, but you are only adding a fraction of the total fermentables, so it will not increase the body much. The reason it's so thin is the amount of sugar added, which contributes alcohol only and adds no body. Carbonation will change how it tastes. Usually it adds some mouthfeel, so it will only help. You'll get this batch drank up in a month or two and be on to the better unhopped extract kits which will be maltier.
Primary #1: Surly Bender clone #2:Berry Rhubarb Wine
Secondary #1: Empty #2: Empty #3: Empty #4: Sparkling Elderflower Wine
Kegged: Dark Side Dunkel, Irish Red
Bottles: Big 50 Barleywine, Framboise Lambic, Dark Belgian Strong, Belgian Golden Strong, Kicked by a Moose Scotch Ale, Apfelwein, Russian Imperial Stout, Barolo Wine
On Deck: Spruced Warmer, CDA