Being on T doesn't magically make our problems go away, but the process of transition, becoming our real selves, can relieve our stress, anxiety, and depression enough to give us the energy to start dealing with underlying issues in new ways. A good therapist is critical for this, but it can work.
I've been on anti-depressants for almost 4 years, following a close brush with suicide, and on T for nearly 2 1/2 years. My therapist says, and I agree, that I'm officially Not Depressed any more, and when he gets back from his vacation at the end of the month, I'm going to start tapering off the drugs -- I don't need them any more. This is probably the first time in my life that I haven't had some level of depression, and it's pretty nice. That doesn't mean that life is rosy all the time, but it does mean that I'm a heck of a lot more resilient, and I have the skills to cope fairly well with whatever comes up.
I'm not quitting therapy any time soon, but my life is very different now.