I have to agree with all those who have already commented. Addiction is not the right term here. Unless one can be addicted to other essential substances, like air or water.
As others pointed out, starting HRT is often a great, practical litmus test for whether one is truly gender dysphoric or might be suffering from some other issue. All I know for sure now is the profound sense of discomfort I feel from current exposure to testosterone at pre-HRT levels, but it makes a kind of profound sense to me that anyone who is deeply dysphoric, especially if one agrees that the cause is probably a prenatal change in brain structures, would tend to find a balance of hormones more in line with those of the gender one identifies with something that is profoundly comforting, helping to resolve so much of what many of us find disturbing without HRT.
When this sort of question arises, I often wind up thinking of Alan Turing, who was ordered to take estrogen by the courts. In his case, the consensus view is that it led pretty directly to his suicide, since he identified as a man whose only "defect" was his attraction to other men.
