Only in a sense that a first order theory of natural numbers does. Really I think it is more accurate to view "a causal model" as a model in the mathematical logic sense -- an object about which logical assertions can be made. In the case of causal models, these assertions are modelling "interventions." Here's a paper on this:

http://www.jair.org/papers/paper648.html

This view appears in Pearl's chapter 7, as well.