Yes, of course. The character is a pretty basic element of the plot. The Little Mermaid trades her voice to become human; then, because she cannot speak, the prince falls in love with somebody else. That provides the major conflict of the second half of the story.
Disney films often diverge quite a bit from their source material, often to provide a happier, funnier, or more comprehensible ending. Aladdin (as an example of a movie from the same period as The Little Mermaid) has a primary conflict that bears almost no resemblance to what happens in the original Arabian folktale. Beauty and the Beast, on the other hand, retains the basic plot of Jeanne-Marie Leprince de Beaumontt's story. The Little Mermaid changes the ending so that the heroine doesn't perish, which requires making her romantic rival into an out-and-out villain. However, the key element of there being a romantic rival is taken straight out of Hans Christian Andersen's original.