I believe Alba can. He really turns Lanvin around in a big way.
And who are the current designers at Valentino and YSL? Whoever they might be, those are also good candidates.
Karl is successful because he respects a lot of Coco Chanel's original designs and really sticks to them, albeit with his own intepretation. Any designer who goes into a big fashion house like Chanel and thinks he or she can forget all the great legacy of Coco Chanel would be making a huge mistake. I don't think Alba will. As a fashion house that is still privately owned, I would say the owners probably have a lot more time to search for Karl's successor than say LVMH.
I always wonder what it would be like to have Alexander McQueen joining Chanel. Of course that would never happen now........