If you are asking about a reference librarian who has helped a student to find sources on the internet, the answer is yes. If the librarian is unable to come up with any sources that are peer reviewed, they should inform the student of that so that the student can try to verify the information. It would, of course, be best for the librarian to find sources that are solidly reputable.
If a student is finding resources for him or herself, the librarian will not be likely to have the chance to tell the student to check. However, if the librarian happens to see a student using such a resource, it would be helpful to warn the student to check for verification.