When you simulate a circuit with Spice, whether it be in Eagle or anywhere else, it's doing a simulation of the voltages and currents through the various circuit elements.
When you simulate a processor, whether it be an arduino or a PIC or whatever, you don't do anything of the sort. Processors are way too complex and all the voltage and current bits are deeply embedded and of no interest. Instead, you simulate the logical behaviour of the CPU at a register level.
Eagle's spice simulator does have some digital logic capability - which falls somewhere between the two - but it doesn't have a full suite of simulated complex programmable logic devices. That's just way out of scope.
I've done some development work on the GPSim PIC simulator. That does the logical behaviour modelling with no regard for voltages and currents except on the very outside level, where it also does a very simplistic peripheral device model. If you want to simulate a circuit that includes a PIC, it's not what you want (although the tool you do want achieves the goal by embedding the GPSim library to handle the core). Similarly, Eagle is a tool for designing circuits, not a tool for developing embedded code. It doesn't, and shouldn't, simulate microprocessors at a code level.
On the other question: no, Eagle does not ship with a Spice model of every single component in the world ever! Of course it doesn't! If you're using something specific, the manufacturer may have a Spice model you can download. Of course, it's probably for the wrong dialect of Spice but they can usually be translated. Ed is very good at helping with that.