Does the Double Tap perk from Zombies make rapid fire useless?

Double Tapp will affect all weapons, as per the wiki entry (emphasis mine):

Double Tap increases the rate of fire (and recoil accordingly) of all weapons by 33% and doubles bullet damage (2.0 version only). It also allows the player to lay down equipment such as Claymores faster and makes players operate bolt-action rifles, pump-action shotguns (as well as re-chambering them), and Wonder Weapons such as the Wrath of the Ancients noticeably quicker, as well as raising the firecap.

Double Tapp will also synthesize with Rapid Fire, as per this Reddit thread. Rapid Fire apparently adds 10-15% on top of the 25-33% boost provided by Double Tapp.