Yes, the DM also back up the apps you have including the ones that you installed outside the App World. Let's say you buy an app from crackberry, it won't be on App World account, but still the DM will back up the app on your computer if you choose to do a complete back up.
I have found easier to back up and restore apps with BBSAK
I tried the BBSAK and it locked up everytime just before completing a backup. If you're worried about your 3rd party apps, the DM software has an option to do it and it works fine.
I always do the "Device Switch" option in DM, then find the temp folder (when it says to connect your new phone), make a copy and then cancel the switch. Mind you, I haven't updated DM in a while, so maybe I'm just wasting my time lol.