That would be quite funny to try and make water run through the whole machine. You would have to actually model some pump mechanism to push the water through the pipes. It’s not totally impossible but super-tricky at best. (Not sure I’m monomaniac enough for that.) And in the end, you’d realize that you can’t make the water change of color to become coffee that falls into the pot… So… No. Bad idea.
As for particle systems. Hmmm… To simulate a small dripping maybe but not a flow of coffee falling from the filter.
I don’t know how the water actually behaves in a Moccamaster but if it’s quiet enough, I’d go for a simple animation for the water container. You can use particles if you need to add bubbles and dynamic paint to make waves at the surface. The same but in reverse for the coffee landing in the pot. In between, it depends on how much liquid you can see but a fluid simulation will probably be needed.
The managers of this brand are real control freaks. No interesting images about Moccamaster on Google Images. The only ones you can find seem to come from a clone factory. Surreal… or creepy!