In upcoming episodes, we'll get to see a scene where White Woz will be talking with Black Woz. This will most possibly be in episode 30. According to the scan, it confirms that White Woz has some other motive than helping Geiz become the Savior.
The scan also says that the Oma's Day will greatly effect the existence of both the Woz. Either there will be the new future where Sougo becomes Oma Zi-O ("Grand Zi-O" of course) or the Future where Geiz becomes the Savior.
I can see that they are hinting that only one Woz can survive depending on the future. So since we know that this is show of Zi-O and he is going to be Grand Zi-O, White Woz might disappear from existence.
Videos by Cast
Sougo Doing Push Ups During the Filming of Zi-O
Seiji Takaiwa Taking Break During Filming of Zi-O
Eitoku doing Push Ups during Filming of Zi-O