Not really. I think there is a difference betwween your consciousness existing in a branch where the casual chains leading to its destruction merely haven't reached your senses yet, and your brain existing in an unchanging state for a long period of time that would stretch the possible restoration of "you" over all branchings forward from the time of successful preservation.

Your consciousness not "running" at all seems like a very different thing from it merely not knowing which branch(s) it is "running" in.