I know that mine did. I used to say "Hi Baby!" to her all the time. When she was born and was upset I would say "Hi Baby!" and she'd calm right down. This worked for 2-3 weeks maybe.
My 3 month old daughter knew my voice, but didn't recognize my face when I shaved my beard. She would turn to see me when she heard my voice, but cry when she saw a stranger.
My second daughter easily recognizes her older sister voice at birth. My older one spoke to her constantly in the womb (usually asking her when she is going to come out and play with her). The best way to stop her crying is to ask my oldest daughter to sing to her (works better than my singing/soothing)
My mother says the same about me. She used to listen to a particular song when she was pregnant with me. After I was born, whenever my dad played that song, I would search for the source.