It depends on the type of case. For a divorce, you will have to appear in court once, so the judge can review your mediated agreement to ensure that it is fair and reasonable. When an agreement and all the requisite paperwork is submitted as an uncontested Joint Petition for Divorce, the court will schedule a hearing a date for your agreement to be reviewed by the judge. While no-one enjoys appearing in court (except lawyers), generally if there an agreement, your “case” will be called quickly and your day in court will be brief.
For other instruments, such as mediated agreements for modification, the courts have a process for approving an agreement without the need for either person to appear in court! As long as the requisite paperwork is filed, the judge can decide to administratively allow a modification agreement without anyone appearing in court.