I can kinda see it both ways.
Part of the issue is that Locke and Celes don't get to spend a lot of time together. Locke saves Celes from the guards and then Edgar warns Celes that this doesn't mean Locke has feelings for her, and she shouldn't fall in love with him.
She insists that she's not going to just start crushing because he rescued her, but the game never really provides an alternative explanation for why she does end up falling hard for Locke. After the battle, Celes and Locke are both optional party members and so don't actually have any shared scenes until the Opera House, which makes them mandatory.
The closest thing they have to romantic development is that they can both be in the party when you find Kohlingen, and if Locke's there, you can learn about his past with Rachel.
And by the time the Opera House rolls around, Celes/Locke is clearly played as a confirmed ship with the pair having feelings for each other. So. I guess she really is that giggly schoolgirl who just starts swooning over a savior.
The Opera House is the first and last time that Celes and Locke actually get to be cute and shippy together. After that, Kefka tricks Locke into thinking Celes betrayed the team at the Magitek Research Facility and the two end up separated.
They reunite on the mission to Thamasa after the Empire feigns surrender, but spend the whole mission giving each other the cold shoulder. Celes doesn't actually come back until the Floating Continent rises, the very final stage of World of Balance. Which is another optional party sequence, so no real Celes/Locke development there.
Then, in World of Ruin, Celes is now so in love with Locke (for, and I cannot state this enough, some reason that is never elaborated on) that he becomes her guiding light. The sight of his bandana on a seagull gives her hope for the world and inspires her to set out and find him.
She does not. Her time as player protagonist reunites her with Edgar, Sabin, Setzer, and briefly Terra. And it ends with the Falcon rising, at which point she retreats back into Optional Party Member status. The game opens up so that any objective can be pursued in any order and with any character.
Nonetheless, it should be said that she moved heaven and earth to find Locke.
While Locke forgot about her and instead moved heaven and earth to find Rachel, the one woman he actually loves.
Finding Locke is a late-game objective requiring at least eight party members to have been recruited, which leads into the outcome for Locke's personal arc.
Locke uses the Phoenix Magicite to briefly resurrect Rachel, and it's Rachel, not Celes, that pushes Locke to get over Rachel. Rachel tells him "I love you, I don't blame you, I remembered you in my final moments and our love made me happy. But I have to die now, and you should give your feelings to your true love Celes!"
Then she dies again and Locke, feeling complete, goes upstairs to where Celes is just waiting around look a good backup girlfriend. They hook up and live happily ever after, the end.
So it's kinda both. Celes seemingly falls head-over-heels in love with Locke right after South Figaro despite her conversation with Edgar, and remains hopelessly devoted to him throughout the rest of the game while Locke waffles back and forth.
There is a lot of emphasis on Celes's feelings but not a lot of real exploration of them. Just that she has feelings and they are what drives her to find hope in a hopeless world. She kickstarts the effort to defeat Kefka because she loves Locke so, so much.
Meanwhile, what feelings Locke has for Celes are never really dwelt on in any capacity after the Opera House, save for the Will They/Won't They cold shoulder exchange he has with Celes during the Thamasa mission.
Rachel just tells him, "Ac-tu-ally you're in love with Celes, go be with her," and then he does, and that's that for his side of the romance.
So there's kind of a weird dichotomy there where Celes puts in so much effort to getting Locke even though there's no clear indication of why he matters so much to her so quickly. Then, against all odds, she actually gets her prize at the end of it all.
While Locke puts in no effort and just sort of wins Celes as a Quest Completion Reward.