I’m not sure what you mean by a “complete church.” My understanding is that the RCC recognizes your particular churches as valid. They are churches in the full sense of the word, which may be what you mean by “complete.”
Imagine a scenario whereby the CC admitted error and was reconciled with Orthodoxy. Would the Protestant denominations then become reconciled as the reasons for ‘protest’ would no longer be valid.
I personally would certainly become Orthodox in those circumstances. And conversely, if a significant portion of Orthodoxy was reconciled to Rome, I’d become Catholic.
I believe firmly that the Catholic-Orthodox split is the only sufficient justification (if it is sufficient) for the separate existence of Protestantism.