You would be correct.

The allusion to 戦国 was made pretty much since the beginning of the period by the people who lived through it, and the people who used the term were consciously comparing Japan of the time to China's Warring States.

The oldest known (to me) would be the Shōdan Chiyō (The Fundamentals of Governing According to the Lumberjack) a short treatise on politics and governing presented to the shōgun in 1480 by the retired regent and probably foremost scholar of his time Ichijō Kaneyoshi.

当時の守護職は昔の国司に同じといへども子々孫々につたへて知行をいたす事は春秋の時の十二諸侯戦国の世の七雄にことならず

Though at current times the shugo's job is the same as the kokushi of old, the fact that their realm pass down through sons and grandsons is no different from the twelve lords of the Spring and Autumn and the seven hegemons of the Warring States.

Then a quarter of a century later in 1508, when an ex-shōgun who was deposed in a coup came back and ran the reigning shōgun out of town, the aristocrat and (then) retired regent Konoe Hisamichi wrote in his diary:

抑世上之儀併如戦国之時何日成安堵思哉

In any case the state of the world is comparable to the time of the Warring States. Oh when will I get some peace of mind.

The comparison was not lost on the warriors as well. Per article number twenty of the Law Code of the Province of Kai issued by Takeda Harunobu (Shingen) in 1547:

天下戦国之上者抛諸事武具用意可為肝要

As the world is [in a state of the] Warring States, all other things should be set aside and the preparation of arms and armors is to be the most important.