Yes.
All Weapon Camos will carry forward into Modern Warfare III. Limited-time Event Camos that were available only during a certain period are accessible if you unlocked them in Modern Warfare II at that time.
Example: A MWII player has the universal Camo “Dark Bones” (above) that was earned during the MWII Season 03 Reloaded Camo Event. They can equip this Camo to any MWII weapon, providing they unlocked it during the time of the Event. Note that “universal Camo” now means “universal to MWII weapons”
COD MW3 Bot Lobby, Boosting, Accounts