No. Spirula spirula is a coleoid, and probably related most closelyto the cuttlefish (though that is not certain). Fossil spirulids are known from the Pleistocene of the Canary Islands, the Pliocene of New Zealand, and the Miocene of Japan. The probable ancestors of Spirula are known as far back as the Eocene, which begin coiled like Spirula but straighten out later. A key difference between Spirula and ammonites is the way they coil. In Spirula the coiling is endogastric—i.e., under the animal. Ammonites, in contrast, have shells which are exogastrically coiled—i.e., the shell coils over the back of the animal. Also see Ammonoidea and Neal’s Ammonite Gallery. There is a nice collection of online images of ammonites on the Ammonites at the Black Hills Institute web page.