Thank you. This is interesting. For the most part we work in UTM zones so our linear units are meters. If we change the page units, does that affect this? At any rate, hoping Esri will do something to make this not so unclear.
First, to answer the question directly above, changing the units of the scale bar should only affect the scale bar. It will not affect your map or any other element on your map. Only the scale bar.
The units available to the scale bar are taken from the list of Distance units. Though we have many units to choose from we chose only a subset for the default list. Unfortunately, Nautical Mile is not a member of the default group. As Thomas Colson highlighted above you can add Nautical Mile to the list of Distance units. It from this list that appropriate unit drop downs, such as Scale Bar units, draw their units. Currently, this is a project setting and any customization is only available for the particular project.
You can use templates to streamline this process.
If you want to have Nautical Mile as a Distance unit automatically available for new projects I would recommend either creating a project template (.aptx file) where you have already added Nautical Mile to the list or saving a layout template (.pagx file) where the scale bar has been previously configured for Nautical Mile.
In the layout template case, existing scale bars that are part of the layout template that was originally created & saved with Nautical Mile as its unit will be in Nautical Mile. However, using a layout template will NOT change the default Distance unit list. Therefore, the drop down in the scale bar pane will not show Nautical Mile. This should not affect the accuracy of the Nautical Mile scale bar. It ONLY affects what units are available in the drop down.
For information on project templates please refer to Create a project template—ArcGIS Pro | ArcGIS Desktop. For information on how to use a project template see Create a new project—ArcGIS Pro | ArcGIS Desktop. For more information about layout files see Save a layout file—ArcGIS Pro | ArcGIS Desktop.
Hope this helps.