UPDATED INFORMATION: Yes for Base Camos.
Modern Warfare II Base Camos can be equipped on Modern Warfare III weapons, and vice versa. However, Completionist Camos (Gold, Platinum, Polyatomic, and Orion) can only be applied to the MWII weapons you’ve completed the unlock for, and cannot be applied to MWIII weaponry.
Note: MWIII is set to include its own expansive set of Camos, including completionist Camos (separate from the MWII Gold, Platinum, Polyatomic, and Orion, above). These MWIII Camos cannot be earned for MWII weapons.
COD MW3 Bot Lobby, Boosting, Accounts