There's the ":a" command, but that's multi-line, and argdo asks you for the text again for each file.
The docs mention the global command (g/pat/command) that will use an alternative version of ":a" that is terminated by a newline instead of by "." on a line (you can include newlines by escaping them with "\"). But I couldn't get this to work.
The only way I've seen is to first yank the text-to-be-added into a named register, then use:
:argdo put x " where x is the register
I'm hoping for something like
:argdo append myTextHere