Correct, unless that box is ticked any PMs you send to others (whether it is a new message or reply to someone) a copy of your sent PM will not be saved for you to view.
I got tired of having to remember to keep ticking that box when sending out PMs that I found a way to permanently check that box, so all my sent PMs are automatically saved.
Hover over the "Profile" in the top menu. A menu will pop up. There click on "Account settings".
On that page hover over "Modify Profile" (highlighted) in orange. A menu will pop up. Select "Personal Messaging".
On the next screen tick the "Save a copy of each personal message in my sent items by default." box, then click on "Change Profile" button on the lower right. From that point on all your sent PMs will be saved to the place pointed out by nickelplate759.