Since Luffy, Kaku and Lucci are the only confirmed awakened Zoan user, If at all, G5 wearing a white, instead of a black Hagomoro , He is the exception and therefore your argument bares even less substance.
However, G4 Luffy at Dressrosa already was wearing a Hagomoro prior to be awakened and so did Yamato, so there exists no etablished hard coded in-verse rule that confirmes it's automatically Awakening.
You simply want that route to be true, that's all there is to it.