To add a filename to the command line using drag and drop simply drag the file from an application (or the Take Command File Explorer window), and drop it anywhere inside a Take Command tab window. The full name of the file will be pasted at the current cursor position.
Take Command is a drag and drop "client", which means it can accept files dragged in from other applications and paste their names onto the command line as described above. It is not a drag and drop "server", so you cannot drag filenames from the Take Command tab windows into other applications. However you can copy filenames and other text from the Take Command window to other applications using the clipboard; see Highlighting and Copying Text for details.