Not if you carefully follow the procedure outlined in this user tip from wjosten: Syncing to a "New" Computer or replacing a "crashed" Hard Drive. If you're using iTunes 11 you'll want to first go to iTunes>View>Show Sidebar in order to follow this guide.
Edit: Sorry, didn't notice that you were restoring from the backup of an older phone. Before doing so, connect your phone to your computer without syncing and import your photos, as outlined here: http://support.apple.com/kb/HT4083, to avoid losing them when you restore to this backup. You will lose the app data from your current phone when you restore to the older backup.
Message was edited by: randers4