it won't have them automatically downloaded, but if you register it to the same account, turn on wireless and sync (menu option or icon) they'all all be available to download from your account unless they're from a source other than Amazon
If I trade in my old Kindle, get approved, get the discount, and order a new model, will the new Kindle contain all my old books? I'm sure the answer is yes, but it doesn't say so anywhere.
No, the new device will not 'contain' your books. Content isn't transferred between devices but items purchased on, or saved to, your Amazon account are available to be downloaded to the new device once it's registered to the same account (as your old Kindle E-reader).
Just to reiterate/reinforce what CBR said -- if you have *any* items on your device that you did not buy from Amazon (e.g. books you've gotten somewhere else and transferred directly from your computer) and they are not in your Amazon account (having been "sent" there) -- be *very sure* you have backups you can then transfer to your new device.
Check your MYCD page (see "docs" for those non-Amz items) to see if they are there.
Then check again.
Check your computer files for such items to see what you have/haven't sent to Amazon.
Then make sure you have *another* backup of everything anyway. (good idea even if you don't buy a new device)