It will back up all the paid apps, they will show in his marketplace, the free ones will not though. Sometimes its a good way to clean up the phone, I often times forget some of the free apps that I had, because I never used them, so they dont end up getting downloaded again.
It will very much so show ALL of your apps (paid or not) in your downloads section. As long as you sign in with the same account you downloaded them with.
Trust me, I've gone through a few of these things.
Funny that when I wiped to factory this morning, and went to download it all my free apps weren't there
I've done it a time or a hundred, and never have they appeared in that list in the marketplace.
What was your process!??!?