Jake Gyllenhaal had never been in a musical before LITTLE SHOP OF HORRORS and not only did he received glowing reviews, but he went on to give a gorgeously sung performance in SUNDAY IN THE PARK WITH GEORGE that matched Mandy Patinkin's brilliance.
As others have said, Ambrose has a training as a singer and has performed live before. Just think of the fact that her audition for FUNNY GIRL was impressive enough that Sher cast her over vocal powerhouses like Stephanie J. Block and Leslie Kritzer. I can't imagine she would audition for MY FAIR LADY if she can't actually sing the role. And for anyone who's not familiar with Ambrose's genius skills as an actor, do yourself a favor and watch SIX FEET UNDER. I saw her in EXIT THE KING and she is a natural on stage. If she ends up playing Eliza by some random chance (random in the sense that she wasn't in the conversation until very recently), she's going to surprise a lot of people who are skeptical about her ability to embody the role. I still wish she had done FUNNY GIRL as I thought it was one of the most exciting, surprising casting choices in recent memory.
"Some people can thrive and bloom living life in a living room, that's perfect for some people of one hundred and five. But I at least gotta try, when I think of all the sights that I gotta see, all the places I gotta play, all the things that I gotta be at"