No, the thumbnails will not remain ‘live’. Any content that exists in the Revit model will be displayed in Project Mode, however, if there is new content such as a view or a sheet, Project Mode will show a blank thumbnail displaying the name of the view, sheet, family etc until a thumbnail is generated. They are not a “live” view of the content, they are a snapshot in time that reflect the state of that content at the time of generation.

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