No, it wouldn't be the "completion of my womanhood." I don't need a man to validate my womanhood, any more than a man needs a woman to validate his manhood. Just being seen as female, especially by other women, is more than enough for me to feel like my womanhood is complete, completely irrespective of relationship status or surgical status or any of those other artificial statuses.
A ring would be a wonderful shiny object that I could fawn over, though. And I will admit, I love me some shiny objects.

(Cubic zirconium is more than shiny enough for me, though. Diamonds are just overpriced human-exploited corporate BS. They look exactly the same and cost 10X as much, plus with the added guilt of the whole blood-diamond thing.) What really matters with any jewelry, though, is the whole symbolism that someone loves you enough to give that to you, and you'd probably think of them every time you look at it. That is admittedly pretty sweet and romantic.
(Side note: Ironic that I think that, because the last time I was in a relationship, we mutually agreed on no jewelry. But I can't help it. I LOVE jewelry now that I can actually wear it.)