No because it's not a text/console window, it's a graphics window that happens to be rendering text.

Thanks for that explanation, jmarsh. Is there a way, within DosBox, of opening a child text-window e.g. command.com /c <program name>, or would that just open another graphics window?

No. You can run a program with stdout/stderr redirected to a file, but that's probably not going to help if it's interactive or you're trying to capture some dynamic output.

You could try vDos (www.vdos.info), it supports copying/pasting text DOS to Windows and vice verse.

Since posting the question in my original post, I have discovered that there is a fork of DosBox created by Wengier Wu, which supports copy-and-paste to and and from the DosBox window. Selection is by mouse RIGHT-click and selection alone suffices to copy the selection to the Windows clipboard; it is not necessary to press Enter after selecting the desired text. Wengier's version was developed primarily to add Long-File-Name support to DosBox, but it adds other things too, like this feature. It is described in this article and the download link for it is: https://bitly.com/12jANWF