If "Review Membership Requests" is checked, then yes, the request should appear in the FBA Membership Request Management area. The user registering should also get an email stating that their membership is Pending. If they don't get the email,
then something is amiss. Most likely having to do with the email configuration in SharePoint or the Relaying setup of your SMTP server. Check the SharePoint log file, which should give more details on the issue.