Yes & No.
In this case, no: http://www.mobar.org/formal/ch02.htm
In this case, yes: http://www.ncbar.com/ethics/ethics.asp?id=279
(It states..."Opinion rules that a lawyer representing a minor ...may only disclose confidential information to the minor's parent, ...if the parent is the legal guardian of the minor and the disclosure of the information is necessary to make a binding legal decision about the subject matter of the representation.")
But for a full list of cases that will side "yes or no," in various circumstances, see "When parents want to know: responding to parental demands for confidential information" at http://www.thefreelibrary.com/When+parents+want+to+know%3a+responding+to+parental+demands+for+...-a096194766
There are a whole lot of exceptions to this "confidentiality privilege." In short, it's best if a minor assumes that info will reach the parents. It's not often that it does, but since it happens, one should be prepared for that event.
See [http://www.ncbar.com/rules/rules.asp?page=9] that shows everyone is subject to losing confidentiality based on these 7 points.