Yes. Mugen wouldnt constantly risk his life constantly and run to her rescue if he didn't care. He isn't doing it out of honor. He gave up his sword for her safety. It was her voice that brought him back from the dead. Fuu's feelings were obvious by the end, rejecting Jin's offer to stay with her. Jin knew she wanted Mugen to rescue her, which is why he told him to go.
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Fuu and Mugen share a complex relationship in the anime "Samurai Champloo." While they may not openly express their feelings for each other, their bond grows stronger as they journey together and face challenges. Their dynamic is one of friendship, loyalty, and mutual respect, rather than overt romantic feelings.