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I personally think that it does by maintaining a more consistent alignment, specifically camber, in the front.
Here's a simple test....With the car on the ground, measure the distance between the two front (or rear) upper a-arm bolts (ie measure across the car). Now jack the front end of the car up and measure again. You'll find that the measurement has changed. That is chassis flex. With the camber brace tying the two sides together, that flex is eliminated (and C4s need all the help they can get!).
There's no doubt it does flex but does it flex that much going around a corner? How much it moves by jacking it up and going around a corner could be very different.
I notice it more on low speed (30 to 60 mph) autcross events than on high speeds. I think the tighter turns on a low speed are where it really helps. I know I felt a difference because I had to do a repair at an event and had to pull it out and didn't put it back in. The co-driver noticed and mentioned it felt "looser' in front. I didn' tell her the brace was out of the car.
All that being said, I don't think it's worth the effort / cost for a street car.
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