So, I have been singing my whole life. Now I am not a professional singer by any stretch of the imagination, I have had many years of vocal training and over 30+ years have developed quite a vocal range. So while I can pull off a passable Amy Winehouse, Sarah McLachlan, or k.d. lang cover, it really has not impacted my speaking voice. This is probably because we sing from a different place than we speak.
So I have learned to intonate and place my singing voice in the proper head space to mimic the sound of many female singers, I am just not able to do that while speaking. What has helped me the most so far as been speaking with less chest resonance (more voice forward in my head) and speaking with the mannerisms and cadence that women naturally speak with. This takes practice, and it still does not remove my voice's natural tendence to drop into a lower register if I am upset or angry.
So while singing can help one sound more feminine, women do not sing their way through life, like in the Sound of Music or Glee

I say, if you want to learn to sing, DO IT!! Singing is fun and liberating.
Best wishes to you supergirl!!
-S