"Everyone wanted to see EDNA, not just CHAPLIN." - from Walk of Fame
Yes, there were many fans who came to see Edna Purviance, and not just Charlie Chaplin. Edna was a big star in her own right during her film career. Like Chaplin, she had fan letters from around the world.
Even today, she is remembered by fans, worldwide. Any country that Chaplin's films shown, Edna was gathering fans of her own. (As did other players in the Chaplin company.)
But Chaplin's shadow was so big, people sometimes forget.
Edna wasn't an independent star (like Mary Pickford), but well loved around the world, as Pickford.
But Chaplin wasn't always generous in talking about his players and people who helped him along the way. Newspaper articles and ads would focus on Chaplin, and not as much (to not at all) on the others who played with him. It was a treat to see the others mentioned and movie posters were the best at showing the other players in the films.
But Chaplin was into marketing his brand name Charlie Chaplin, and the people who worked with him, knew that. Chaplin was never into making stars, he was into making stories on films. The people who became stars after first working with Chaplin, had their own personal drive to continue on in the business. That is why some were more successful, than others.
As for Edna, she was never as interested in the 'star' part, of her career, but at the same time, appreciated her career very much.