I do not think so.
I think number of successful "Sand v Mist" PvPs will be compared against number of successful "Mist v Sand" PvPs and that will determine the winner.
Again, I think.
I also have had the problem of (ENEMY!) appearing randomly.
I have a Mist character, that logged out in Sand before the war began. I go to "slay in the fields" and I see Lord of SunaGakure with (ENEMY!) (they are a Sand nin), then there was another character that was also a Sand nin (at least according to their bio), but they did not have (ENEMY!) next to their name. Then, in a Sand Dwelling, there was also a char that had "Sand" in the bio, but no (ENEMY!) next to their name.
I'm not sure if it was because they were at a lower DK level or not.