Jane's comment about not telling her parents was written in her first lettter to Elizabeth about Lydia & Wickham. Jane thinks that they have gone to Gretna Green to be married, and at this point has no reason to think otherwise. The rest of the family seems to think the same. She is glad that her parents were spared the knowledge of Wickham's bad character since he will be (or already is) a son-in-law.

As for whether telling Mr & Mrs Bennet about Wickham would have prevented the elopement, I have some doubts. Mr Bennet would not have thought that Wickham would be interested in Lydia since Lydia clearly had no fortune. After all, Wickham had deserted Elizabeth for Miss King, so why would he be tempted by Lydia.