I just tested it from my addon which using a Multiline Editbox without an issue. However, I'm on Linux which uses '\n' as the EOL. Windows uses "\r\n" -- I'm not sure if that could be the issue. I can say for sure that the '\n' characters are copied to the clipboard though.
So either your browser is stripping the text of the new-line characters when you enter it into the field (if it's not a multiline editbox), or your browser is expecting "\r\n" as the EOL. I have seen many instances where edit boxes inside windows apps (as in in your browser if you're on windows) will display everything on a single line if it only has '\n' instead of "\r\n"
Is it possible to delimit the list with a comma or semi-colon instead of new line when copying it to your browser? It'd increase the portability of your addon.