You can't batch edit with an action in any version of Elements. You would need to write scripts for that purpose.
You might have a look at an affordable external add-on called Elements+. It offers a lot of scripts for batching common commands, and advanced users can even customize the scripts.
If what you want is to apply the same set of edits to several images, that's something you can do by opening your files at the same time in the ACR dialog. You can always apply the same edits than the previous file by choosing the 'previous conversion' option.