Glad to see my comment was reviewed positively. I guess I will stay.
No this does not count as puberty. Puberty is an internal process that starts in the brain. Puberty blockers not only stop the body from changing but it stops the brain development as well. Jazz still has a prepubescent brain, which may explain her immaturity. Perhaps her brain is a bit more feminized because of the estrogen, but that just means she has a feminized prepubescent brain, not an adult brain.
Giving a prepubescent child estrogen does not turn them into an adult woman. The hormones simply cause the body to react in a certain way. Just like how some babies are born with breasts and can even lactate and some newborn baby girls can even have "periods" because of the hormones they are exposed to in their mothers womb. No one would ever consider these changes in newborns to be puberty.
Estrogen will not give Jazz a sex drive anymore than it would give a newborn baby washed in it's mothers hormones a sex drive. Because again, the sex drive comes from the brain and her brain has been prevented from developing. Even masturbation will be a problem for Jazz because the penis develops more nerve endings during puberty. This is one of the reasons why boys become obsessed with it during puberty. It becomes more pleasurable to touch. Jazz will never feel the same level of sensation as an adult male because she has had no development. And on top of that estrogen dulls the sensation in the penis. It's also worth mentioning that whatever Jazz feels now, is the most she will ever feel after the surgery,
The testosterone cream might help, but even then. That still won't give her a sex drive. It will just give her more sensation down there.