public sealed class UnknownDatastore : Datastore, System.IDisposable  

public async Task ObtainingGeodatabaseFromProjectItem()
{
  IEnumerable<GDBProjectItem> gdbProjectItems = Project.Current.GetItems<GDBProjectItem>();

  await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
  {
    foreach (GDBProjectItem gdbProjectItem in gdbProjectItems)
    {
      using (Datastore datastore = gdbProjectItem.GetDatastore())
      {
        //Unsupported datastores (non File GDB and non Enterprise GDB) will be of type UnknownDatastore
        if (datastore is UnknownDatastore)
          continue;

        Geodatabase geodatabase = datastore as Geodatabase;
        // Use the geodatabase.
      }
    }
  });
}