I have a female Japanese friend that I call "~ちゃん", even though she is a little older than I am. I thought one of the purposes to use "ちゃん" is to emphasize cuteness. Am I right with that?

Emphasize cuteness? I am nowhere near being cute; in fact, I wear a full beard and look like a Japanese Leland Sklar. Regardless, some people that are younger than I do address me with 「ちゃん」.

When an adult is addressed with 「ちゃん」, it is not so much a title as part of a nickname. Even if the 「～～」 part of 「～～ちゃん」 is an actual name, the whole phrase is being treated like a "nickname" of affection. At least this is how I feel as a native speaker.