No, it is not possible to view duplicate layers offline in ArcGIS Field Maps and this is a known limitation. When viewing a feature layer in ArcGIS Field Maps, a mobile geodatabase is created to store the layer within the device that syncs to the unique replica on the hosting server (ArcGIS Online). So when creating a duplicate layer, an identical mobile geodatabase is created on the device and both layers attempt to sync with the same replica. However, only one mobile geodatabase is synced to a unique replica at a time and the machine only recognizes the original mobile geodatabase and syncs to it. Therefore the duplicate layer cannot be viewed.
As a workaround, create and add a view layer to the web map. In doing so, both the original layer and view layer are connected to different, and unique mobile geodatabases. Refer to ArcGIS Online: Create a hosted feature view layer for further instructions.
Note: When updates are made to the original or view layer, they may not be in sync despite originating from the same source data. This is because they are connected to different mobile geodatabases, and require multiple syncs to display correctly.