If so, how do you measure the effect?
tl;dr: by measuring the tension between the unbraced mount points.
Today, I installed a Whiteline rear strut bar on my 2004 WRX wagon. The car has 162K miles on the odometer and has always seemed in need of a little more stiffness in the area of the rear seats. There's a large volume back there without any sort of cross bracing (unlike a sedan) and the brace certainly seemed worth a try.
In the spirit of my original question, however, I wanted to see if I could measure the effect on the chassis in a static scenario. I tried two situations: flat on four wheels and with the driver's side rear wheel on four stacked 2x10 boards (which puts the wheel about six inches above the ground). I installed the circular fittings on the car and attempted to collect some reference imagery along with a little qualitative data.
NOTE: yes, in an optimal world, I would have used steel wire and a tension gauge. In the spirit of run what you brung, though....
First, leaving the wheel flat on the garage floor:
What you see there are the connecting holes on the braces with a double line of fairly hefty paracord running between them and tightened with a trucker's hitch. I added the sticky pads for some visual reference at the time. I later added the green line from the bottom of both connecting holes using Paint.net. If you've used a trucker's hitch, you know that you can get the line pretty taught: it made a solid "bwong" when I flicked it.
Here is the equivalent image when one wheel is pretty high up, balanced on some quite sketchy lumber:
This picture is both disappointing and satisfying at the same time. The car clearly isn't made of rubber and tin foil (that's good) but it's also not showing an obvious flex that I could use to say "see? this was clearly money well spent and I am a genius!" Sadly, if you zoom way in, you can see that the front line looks largely the same as in the first image.
What is less obvious is what's going on in the rear line (the part where the knots are). That line is showing some droop (a bit but it's there). What you can't see at all is the change in tension in the line. Whereas before I had a nice "bwong," at this point it was definitely mushy.
At the end of all this, I think I can conclude that, yes, for this specific car, I can measure a definite opportunity for improvement in chassis rigidity that this part will address.
Later, when it's not the snowiest goddamn winter that the world has ever seen, I'll see if I can find a way to measure differences in handling that don't involve me being a huge donkey on public roads.