I agree with some of you and disagree with some others. What I'm surprised about, is how quickly some of you form up your own theory from bits and pieces of basic theories from Wikipedia, which is in itself not bad at all, but rather the way you confirm its truth rather way too quickly purely because it satisfies trivial common sense. Now this particularly does not work very well for fluid dynamics, because in reality it is necessary to take an object's shape into consideration...hence the only proper way of doing it would be calculating this 'black magic' numerically (Computational Fluid Dynamics) and test it in practice in windtunnels.
One theory I see in this topic that will satisfy common sense, but unfortunately is untrue is that smooth airflow means that there is less drag. One famous(?) counter example is the golf ball: a ball with dimples compared to a perfectly smooth ball will have far less air-induced drag, while its airflow is absolutely far less smooth at the same time. The reason is that with the dimples, a small boundary layer of turbulent air (meaning chaotic) is created that actually helps the ball travel further. The surrounding air therefore gets less of a chance to take away kinetic energy from the ball.
Another thing is that people will think that a square object will always be less aerodynamic than a pointy thing, which is also incorrect. The Nissan GT-R is a perfect example of this being false, mainly because a lot of aerodynamic drag is not only dependent on the frontal area, but also how the airflow is over the car beyond that, even for a few more metres behind the car. A droplet shape would be one of the most aerodynamic shapes for a car to have and that's why a Porsche 911 is relatively efficient on this matter. The reason that the shape of the back is the most important in a design is the formation of complex air vortices, which dissipate energy. Now the thing is, the effect is entirely the opposite of the golf ball: the formation of air vortices now substantially creates extra aerodynamic drag. Why? Because the vortices aren't nicely arranged in a nice boundary layer this time, but also simply because a car is never shaped like a ball.
The only correct conclusion therefore is: unless you can perform CFD calculations in your head, it's impossible to say anything about aerodynamic drag purely based on 'common sense'. The subject of aerodynamics is as super-counterintuitive as you can get, really. My advice: throw the common sense out of the way and only base your conclusions on real-life examples and calculations when talking about aerodynamics.
Now to answer the main question: a flat floor and diffuser on a car add both downforce and aerodynamic drag, so qualitatively GT6 has this modeled correctly.
The excellent real-life example of Ridox2JZGTE also underlines this.
Also, I have a bachelor's final report of a friend of mine here which is about the design of the undertray of a Formula Student racing car, which include numerical calculations. The conclusion is that the floor and diffuser do create more drag while contribute to more downforce. The reason: air underneath the car accelerates enough that it falls into the turbulent region (high Reynold's number); the turbulent airflow dissipates energy and creates more drag. The higher air velocity goes hand in hand with a lower pressure area beneath the car, creating a net negative lift (downforce). Key note: this conclusion can only be accepted for a car of 1:1 size, because the effect of airflow over a much smaller object can be vastly different. And even more so when the shape is different. But generally, unfortunately a flat floor will create more drag on a car.