From how I understand it's supposed to work, unless you explicitly hide your email address, QuickMail is supposed to send in a way that the end-users can reply to the email and have the email go to the sender. However, for some reason, all emails have both a "from" and "reply-to" of the noreply address:
To: Christopher Myers <CMyers@millikin.edu>
From: "Christopher Myers (via TEST)" <firstname.lastname@example.org>
Reply-To: Do not reply to this email <email@example.com>
Subject: [3.3 Test Course] Test email from Moodle Test
X-Mailer: PHPMailer Moodle 2017051503.01 (https://github.com/PHPMailer/PHPMailer)
X-Moodle-Originating-Script: https://moodletest.millikin.edu => MUWACTEST:blocks/quickmail/email.php:363
We've tried upgrading to the latest version, and it hadn't made any difference. I'll attach some screenshots for you as well.