With the revelations from 6.4 and the careful method in which the Echo Flashback was presented, if there's anyone who is supposed to be recognized as the 13th's Ardbert, it's the original Golbez. But I don't think that matters - Zero doesn't need a piece of Azem's soul to be a hero, not even to have received Hydaelyn's Blessing of Light Crystal - all of Ardbert's friends had one and so did Ysayle. If Zero had a Traveler's Ward from Hydaelyn's Blessing it would explain her survival post-Flood and it's the mechanic that undid Fandaniel's full-voidsent transformation on her.

What's up in the air is if in a post-defeat of Zeromus cutscene we directly absorb the soul of the real Golbez trapped in that memmoriate crystal or not, because that plot point has become the Shikon Jewel that we're questing to recombine. Not that it would actually transform us into an Ancient/Azem themself, according to recent translations of Banri Oda's Korean Q&A. But it is plot-explained power-ups for leveling beyond 100.