Interesting idea, but that seems like overkill to me.
Like, yeah, if I was to sign up for Ashley Madison, it would be ideal for me to use an email that is not my known one. ;) But in most cases I don't think that's adding much extra security. If anything, you're more likely to lose access to a site by forgetting what your super secret email for it was than from someone hacking it.
This isn't to say that I'm totally against it. Part of me just feels like there's more that can go wrong doing it that way.