I don't think so. I copy my entire disk drive including the /System/ folder using SuperDuper!. My back-up drive also is a boot drive as a result. Meanwhile, the versions of the apps I run are in my dock, and if I select any of those apps, right click, select Options and select Show in Finder, the executable always appears on my primary disk drive, not on my external back-up drive.
I don't recall what I did to cause the annoying application-has-moved message to first appear, but I have been tolerating it for many months (although I have been using SuperDuper! for years). Also, the message does not appear with any of the other several dozen applications--including another six from Adobe--I run on my Apple computer. It happens only with Dreamweaver. I literally stumbled onto the above series of corrective steps earlier today. I hope I recalled all the steps correctly because--at the time--I really did not think my actions would have any effect. I hope Laurie elects to try the sequence for herself so she can confirm or disconfirm whether they are correct and actually show a repeatable effect.