I was reading all about this fantastic movie today on a blog by film critic/enthusiast Edward Copeland (which I found by way of Roger Ebert's great Twitter feed). Copeland has all sorts of interesting behind the scenes details and stories about the film. But the most surprising to me was that in this film which is all about voice doubles at the start of the sound era, Debbie Reynolds herself had her singing voice dubbed for the "Would You" number! Apparently, the studio brass thought that Reynolds' beautiful singing voice didn't quite match the look of Jean Hagen. So they hired a voice from Disney's DUMBO which was a bit deeper, a woman named Betty Noyes, to do the honors for this one song in the film.
Below are the two clips so you can compare and contrast; the first is the official released version of the film with the dubber and the second clip has the recording of Reynolds singing. All other songs in the movie, though do utilize Debbie Reynolds voice though, notably, none of them are solos.