Yes, "should." I've found that should happen and did happen are two very different things when it comes to a lot of homes.

Incidentally, our roof had gutters/drainage originally. We put in our own french drain after about 8000 hours of research, and decided to re-route the roof drainage to right above the new french drain (separate pipes) because the roof drainage broke at some unknown point and was dumping water around our foundation piers (yay...). Well, our roofers came and installed gutter guards after all this, which caused the gutters to shed 60% of the water into the drainage area because of the way they're angled. If we hadn't put in a french drain, it'd be a real problem, but as it is now, it's a mild annoyance that I keep telling myself I'll fix.