From my experience, when restoring from an iCloud backup (rather than the locally stored one in iTunes) you will regain all your personal data (apps, contacts, all the stuff you care about...), but it does NOT restore either the lock passcode or the restrictions passcode. I would recommend backing up the iPhone to iCloud, then restoring to that backup. Last time I did this I was running iOS 5 & if iOS 6 changes this rule you only lose some time & you'll be back where you started. There may also be a way to delete or modify the file that has the restrictions passcode stored in it, but most likely you will have to jailbreak your iOS Device in order to access that file & that would be more work than restoring.
P.S. For all the people arguing; it is totally possible that someone forgets they made a passcode & also totally possible that a bug in iOS created a passcode, in these forums it is not our job to argue about the cause, but create a seemeless experience of one another helping those in need to get their products to a working condition through the giving of our knowledge, not the fanboying & blaming of our anger.
I appreciate your help, but the thought of restoring from any backup and having to reorganize over 300 apps and my music and it not resolving the restrictions password issue would be far more aggravating than just 'wasted time'. We really need a definite answer before spending hours with the restore process. Thank you for your answer though! :)