In real life the floors help. In GT it's harder to say.
Rear downforce helps all cars, including FF. All four tires are used for cornering and FF's are prone to lift off oversteer because of the lack of weight on the back. Rear downforce will prevent the back end from sliding out during a sudden release of the throttle at high speed and allows you to run more front downforce.
A full flat underbody panel also doesn't produce downforce solely at the rear. It's produced all along the floor. There are low pressure peaks though, usually the splitter and the diffuser entrance. (blue in the image below)
The relative strengths of the peaks can move the center of pressure forward or backward and change grip balance.
This could all mean nothing in GT though. We already know floors incorrectly produce drag, so they may be modeled poorly in other ways. The fact that they add drag is not only bad for top speed, but potentially also for handling. It depends on where the drag force is compared to the center of mass.
Race cars have wings mounted low even though the air is cleaner up high because the drag on a wing produces a moment that lifts the front wheels. If the GT6 flat floor adds drag above the center of mass of the car, you will end up losing some front grip (but probably not enough to negate the benefits of downforce). This can be made up for with some suspension tuning to put less weight on the front tires.
Which ever way the GT floor works, all cars should see a benefit, at least when tuned properly.