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 Charles Perrault'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.