Yes, you can backup the drive, assuming you can get it to bootup and run without getting the yellow light. Sony's User Guide on backing up states:.
Some types of backed up data can be restored on another PS3™ system. The types of data that can be restored on another system are as follows:
- Saved data from PlayStation®3 format software *1
- Image files under (Photo)
- Music files under (Music) *2
- Video files under (Video) *2
- Bookmarks added under (Internet Browser)
- Terms that were added using (Settings) > (System Settings) > [Add/Edit Term], or predictive terms that were "learned" by the on-screen keyboard
*1 Copy-protected data cannot be restored. Also, saved data that has been restored may not be usable in some games.
*2 Does not include copyright-protected data.
Most everything should backup and restore, except copy-protectd game saves, movies, and music.
Your best bet for getting your data to the new system is to transfer the data directly from the old to the new PS3 using an ethernet cable. Again, details in the PS3 User Guide. Unfortunately, both systems have to be functional for this to work. After the transfer, any old backups will no longer work. From the user guide:
If you back up data on a PS3™ system and then transfer data to another PS3™ system using the data transfer utility, copy-prohibited saved data that is included in the backup data cannot be restored on either system.
Unfortunately, you can't just swap hard drives between systems. According to this thread requesting this feature, it looks like the PS3 encrypts the internal drive with a key that is unique to each physical system. This key can't be transferred.
Good luck!
Some PlayStation 3 games have locked game-saves which means their game-saves are tied to the system itself. The result is that if you backup these files in a USB or an external HDD, you won't be able to use them in another system. (This is most likely done through encryption).
Here's a list of games with locked game-saves. As the list states, games without asterisks have files which are locked to the system.
However, there's a way to bring these locked game-save to another system. The PlayStation Plus service lets you upload these files to Sony's servers to be able to retrieve them in other systems. This service is not free.
Best Answer
Yes, as long as you are using the same PlayStation Network account.
Oh, and the 500GB hard drive I just installed is AWESOME!