That is unlikely, from all the references it seems that the Nameless One fought in the war which took place during TRPG2, not earlier (especially as he is quite old, and I doubt he could've participated much in any earlier conflicts, as several decades passed before TSoG took place).
A lot seems to indicate at David: inability to save parents, good scanning (or, rather, anti-scanning) abilities, his knowledge of how to teach different elemental attacks, him being in TRPG2.