Well considering how the Brotherhood was left massivly crippled at the end, (The Dark Brotherhood Chronicles not included, of course.) you never know how things could have turned out. It could have gone either way. I don't know if Cyrodiil's Brotherhood would affect the status of other branches though.
The dark brotherhood, as I see it, is too decentralized to be affected by what happened in Cyrodiil, and probably for good reason.
Also, they need to be like the group in Daggerfall, an organization that has the monopoly of assassinations, and not a bunch of goth devil worshipers. Also, the Morag Tong wasn't that interesting as a group and questwise. I mean, wtf, they can kill people in plain sight! That takes no skill. Also, I'm tired of their so-called "honor." Nothing but a bunch of expensive assassins protected only because Vivec saved their asses after Reman III or whomever was assassinated.