Yes, and no. There was no 'Warriors of Light' at that time, the player was just a regular adventurer newly arrived in town, but during their journey into the city they experience the infamous starshower and hear Hydaelyn's voice, thus awakening them to the Echo. This then causes them to jump in and out of other peoples' memories of ten years earlier when the Archons first arrived in Eorzea under direction from Loiusoix (when the Battle of Silvertear Skies occurred), while at the same time continuing their training as a new adventurer, thus leading to puzzled looks from others when they start rambling on about things that happened a decade before. This all culminates in the player's character collapsing, whereby one of Minfilia's 'watchers' (basically, they were Echo-awoken talent scouts employed by her to look out for those showing signs of the Echo) makes contact with the player's character and directs them to the Path of the Twelve.
The Warriors of Light were never mentioned in 1.0, it was a term that was added with ARR, originally to describe the fighters at the Battle of Carteneau who Louisoix teleported 5 years into the future, and which no one could remember their identities as a side-effect of the spell, only that their faces were obscured "as if by a bright light". Later on the term took on extra meaning and relevance, but in 1.0 the term was never mentioned.
The confusion over this particular point is partially due to SE making allowances gameplay and narrative wise for those 1.0 players who did not achieve a somewhat arbitary accomplishment in 1.0 (passing the Lunar Transmitter battle in 1.0). 1.0 players who passed this fight gained the special 'Legacy' story and opening when they started ARR where they were one of the original Warriors of Light incognito, with npcs eventually remembering their identities by the end of ARR's story.
1.0 players who did not pass this point alas had the same starting story of ARR as a new player, and it was pretty much just handwaved away what exactly you had been doing in the meantime - presumedly continuing training or something. There were some indications the game still considered such a 1.0 player character as being a veteran of Carteneau (remember, there were a lot of fighters and mercenaries there, and only a handful of 'Warriors of Light' teleported, if that), so that is what Louisoix was referring to.
My own personal headcanon as a 1.0 player who unfortunately did not meet the story requirement for the Legacy story, is that my character was at Carteneau (with her Path Companion) but nearly died in the ensuring storm, and was evacuated to the ALC's Guild in Ul'dah along with other wounded for treatment, her physical wounds healing quickly but her mental wounds took a lot longer (including some retrograde amnesia), requiring nearly 5 years to recover properly enough to restart her journey, which is why she returns to Gridania on the chocobo carriage.
That's just my own headcanon though, so other 1.0 players may have come up with different ideas to explain exactly where they were and what they were doing in that intervening period.