…the game takes place during the Ancient Age. Panzer Dragoon’s Ancient Age.
I think it unlikely for a number of reasons, but I can also get to that conclusion by filling in a few gaps with my imagination. 
A thought struck me recently that CD sounds closer to the Dragonriders of Pern scenario. With (SPOILER): the alien planet colonization, and the adaptation of indigenous lifeforms as allies. Interesting enough to me either way, since I might take it as further evidence of Yukio Futatsugi’s inspiration…
That’s a pretty big gap to fill in though, since dragons were only believed to have been developed at the close of the Ancient civilization. A lot of reasons it wouldn’t bother me personally though. 
That’s a good point. The only way I can see around this inconsistency with the theory is for the Ancient records to have been tampered with or purposely written to mislead. Which wouldn’t be all that surprising.
I do like that element of Panzer Dragoon’s backstory though, especially if the dragons were created as a response rather than as part of the initial Tower plan. Or as an alleged response to “protect” the people from Destruction Faction terrorists.