Yeah, Allen has some major connection with his arm-sword, but that doesn't mean that it can't work... just that it wouldn't fail because he doesn't know how to use it. If he's got some other issue, or the Noah are too powerful (there's always the Allen-has-some-Noah-power theory, after all), then he can synchronize with it all he wants, but he can't necessarily do anything.
But why would the Earl give such a gift to Tiki, who clearly liked being a Noah? And why would there be any reason to suspect that they COULD become normal humans again, before Allen's sword came along? Anyway, the betraying gift idea describes Innocence excellently... and Dark Matter obviously doesn't have that kind of automatic mechanism (Cross set the self-destruct button for the converted akuma). I can't see the Earl doing something like that to someone who can't betray him.