I understand that some games have copy-protected saves (like Killzone 2) where you can't copy a save file unto a flash drive. However, I was able to do just that for Uncharted, Batman: AA, Call of Duty World at War, etc.

My question is, if I copy them unto a USB stick and to a new hard drive on a different console, will I be able to earn trophies on the new console if I load my saves and continue playing them (after logging into my old PSN account)?

Should be. Most Dev's soft link em to your PSN login, so you can't share them with others and have them earn trophies. As long as you're using the same PSN name, you're good to go.