You do not need to ask permission before sharing the link.
Some Elite Notetakers choose to inform their professors before sharing, some choose not to. It is up to you to decide whether or not to discuss StudySoup with your professors.
Many professors are very supportive of StudySoup, as it is similar to tutoring. If you are worried about your professor being against the use of StudySoup for any reason, please refer to the following document as a resource for answering any questions from your professors you may encounter: