Yes you can back up your DLC and yes it will be recognized by your PS3, as a side note it will work on any PS3.
They are just .pkg files.
They are stored in some odd location though and I can't remember or find where off the top of my head. I do know that they will be named some weird 00101010-4567677.pkg though.... If you can remember how big they where that would help. (and once you get them on a PC you can rename them with no ill effects.)
I would post some links to some sites but with all the legal jizz Sony has been shooting, its probably best to wait for the dust to settle before I post links.... lol
Edit: I was half awake but, they will work on any PS3 as long as you hex edit out the check... lol