The access rights are respected in the same way as if you would use the Web-Page to post the comment. The authentication is done based on the validity of the E-Mail sender.
In your reply you should take care about the content. We don't strip off any content from the E-Mail. So if you click on "reply", and the original message is appended to your reply from your E-Mail client, you need to make sure to remove this before sending.