The models don't really use climatology; they are dynamical in nature, meaning they see what is going on and forecast from that (whether or not the initial values it gets are flawed or not is another story). Despite no precedent, the dynamical models (GFDL, AVN, etc) shouldn't have any trouble with this, or at least more trouble than normal.

The statistical models -- CLIPER, SHIPS, and so on -- will likely have some trouble, as they rely on what they know. Even the FSU Superensemble, which incorporates a lot of training/climo into its database, will likely have some trouble with such a case.