The problem with that approach is that any good FPS engine is going to be very complicated and do some very tricky things with code. Speaking from experience, if you are not already a fairly good programmer, you're not going to be able to learn anything from something as complex as a 3D engine. The way the code is layed out won't make sense to you, a lot of the terminology will be totally foreign (and impossible to just "look up" easily), and almost everything will be doing things that you're not familiar with and don't recognize. Looking at the blueprints for a skyscraper doesn't do you any good if you don't understand architectural notation.

A much better approach is to take a tutorial program like NeHe and go through it from the beginning. That way, you will be introduced to the concepts, terminology, and methodology slowly and in an order that makes sense. Then, when you have enough of the building blocks, you can build an engine of your own. You'll understand why the structure has to be a certain way, how different elements work and how they interact, and in general you'll be much better equipped to work with such a project.

I'd recommend you go through here if you haven't already. Good luck!

what about this: