I don't think you should use notoriety as a measurement of how likely they are to be companions, though. Fan popularity is very clearly not their priority when determining the party - and by convention, the overwhelming majority of party members are new characters who will need explanations and introductions.
(In this respect, if notoriety meant everything, you could say Cole has a massive advantage over Vivienne, Solas, Sera, the Warden, Iron Bull and DHMG)
If the developers have a storyline in mind for the character, they'll use them - and that bio clearly proves that there was a storyline for Cole, at some point. He even got a class allocation.
And we can't tell what Cole did after Asunder... because nothing in the universe has taken place after Asunder. How can you tell what he did?
Five seconds after killing or abducting Lord Lambert he could've disappeared entirely, only to show up in Inquisition.