"Has it ever been a requirement for either Thénardier to be able to sing?"
I don't think anyone expects either of them to have a pretty voice, per se, but Madame Thenardier is such a low-down, bawdy kind of character, that Bonham-Carter's breathy singing voice doesn't really seem to fit the character. Whenever she sings, it's always a whisper, and this isn't really a whispering type of character.
I do have yet to see the film, so I'll give her the benefit of the doubt, but I felt similarly about her Lovett (which was, in her defense, acted beautifully), but I was not impressed listening to the CD. On the plus side, Anne Hathaway absolutely kills her song. Magnificent.
I am a firm believer in serendipity- all the random pieces coming together in one wonderful moment, when suddenly you see what their purpose was all along.