I don't believe it is a diagnostic tool. People just say that because if someone does not want to be a woman, then any feminizing changes are likely to be horrifying. When I started growing facial hair at 19, I would rip them out with my fingers. But then I told myself, and believed, that being trans or intersex or whatever, was a direct result of my body's inability to virilize to an acceptable extant. To any extant. I never evn had an erection til I was 16, so I lied all the time about mastubation when really I had no idea how or why it happened.
That's a major tangent. The point I'm trying to make is that changes on E are often times slow. I have no idea how fast it reaches the brain and actually don't see how that has any effect on anything since it is hormones and a chemical messenger that awakens (or excites) receptors in the body. Hormone is from the Greek and means "to excite or turn on." Over the long term, I imagine it is quite devasting as can be seen by numerous people forced to undergo hormone therapy against their will. I know one person said to me one time if he really wanted to get back at someone he woul dstart feeding them hormones and then cut off their penis and construct a vagina. Might sound good to you, but to a cis male I don't they think anything is worse.
But any effects won't be noticed for months, excpet for skin which changes quickly. I believe the calming aspect of it is just a placebo effect from finally "doing something"