Google Forms from the Google Docs perspective expects there to be two parties involved in a form submission:
- Google’s Server
- End User’s Client Browser
Because there is a direct communication between Google’s server and the User’s Client Browser, Google knows which submission goes with which client and thus can allow editing of prior responses.
What the Google Forms plugin does, and this is by design so the form can integrated into your WordPress site, is insert your WordPress Server in between what Google “expects” the process to be.
The form content is submitted to the WordPress site which then, using the WordPress HTTP API, resubmits it to Google. This second submission is effectively anonymous as far as Google is concerned because ALL the submissions for the form come from same end user which is your WordPress Server.
The actual end user is abstracted away because that interaction happens between the end user and the WordPress site as opposed to the end user and Google.
So to you answer you question, the “Previous Responses” will work although it will take you to Google Docs. Instead, I recommend using one of the many Google Docs integration plugins to show the results within your WordPress site.
The “Edit your responses” link won’t work correctly and I strongly recommend hiding it with CSS. In fact, I recommend hiding both and having a separate link to the results within the WordPress context.