Regardless of twist rate, target shooting at 200 yards and beyond is very challenging, to say the least. Why? There's a lot of randomness in results at 200, to say nothing about greater distances. But perhaps the interest is in PRS style shooting where the end goal is hitting steel targets at various distances.
As for twist rates, it seems that the prime purpose of faster twists would be to achieve better and more consistent BC in order to achieve better performance with the increasingly anemic performance of .22LR as distance grows. There are a lot of anecdotal reports, but there's not a great deal of published and verifiable information from the results of testing.
Bryan Litz did a study of .22LR twist rates and noted that with the exception of a couple of ammos tested, there doesn't appear to be much to be gained. In Litz's words: "There is generally not a strong relationship between twist rates and BC for most rimfire ammo types in 1:16" and faster twists."
Nevertheless,with .22LR long distance shooting the current trend is to use faster twist barrels. Of course, no barrel can overcome the inconsistencies to be expected even in match ammo.