Is there a way to insert automator output at the cursor?
Could your automator script copy the output to clipboard and then run this script to paste the clipboard contents?

do shell script "pbpaste &gt; /path/to/your/clipboard-file.txt"


This topic covers the paste function in more detail https://stackoverflow.com/questions/9976338/applescript-to-paste-text-from-clipboard-into-a-file