It will distribute but how much depends on how much fat and muscle you are carrying, your genetics, and how much you exercise.
T is not a weight loss drug, in fact, for many it's a weight gaining supplement. While it can assist in muscle building it won't if you just sit around, normally. I have heard of guys getting more muscular just by taking T but I think they are the lucky ones. Also they tend to be the on the more slender side of the weight scale.