Can I see a system clock move forward in time just as it would in a real system?

Yes. This is one of the fundamental features of simulation. The model created by ccProphet is a virtual representation of your center. For example, the queue lengths shown by the model at 10:06a.m.of the simulated day are representative of what would be expected to happen in the modeled center at 10:06a.m.on a real day.