In theory yes, but not in practice. Gaur and Mog for example have just about nothing to do with the main plot. Terra is important early game, but fades into the background and literally becomes optional by the end. Celes on the other hand is consistently important to the story throughout, is always mandatory, and is front-and-center in many of the most iconic scenes (the Opera, the cliff, etc). She also has much better developed interactions with the rest of her party (especially Locke) than most of the others.
Really you could cut the playable characters down to Celes, Terra, Locke, Sabin, Edgar, and Setzer with almost no loss. Among those, Celes and Locke stay consistent in their importance while the others are important for sections of the game but not the whole game.