No, it is not possible to use the World Imagery with Metadata web map as a basemap in the Map Viewer. When the World Imagery with Metadata web map is opened in the Map Viewer, the basemap used is World Imagery. Basemaps do not include the metadata pop-up functionality because basemaps are rendered as images and do not include the attribute information. This is also the case after adding the World Imagery with Metadata web map to a Group used to customize the Basemap Gallery. When the custom basemap is added to the Map Viewer from the Basemap Gallery, the pop-ups are automatically disabled.
However, it is possible to use the metadata available in the Imagery with Metadata web map separately, regardless of the type of basemap, by following the instructions below.