Coyote Squirrel has video up of Johnny Depp singing as Sweeney - both in the studio and in the film. It's just a quick bit, but it shows me that while Depp's Sweeney will not be traditional - dark, rich baritone - it will be musical. And I'm OK with that.
On another note, I've rad in some quarters criticism that Depp is too young for the role, that Sweeney should be older, more middle-aged. To that, all I can say is:
Len Cariou's age when he originated the role: 37
Depp's age when he filmed the role: 44