I was just test riding this new build Centurian that had no adjusters. I had the wheel axles pushed to the rear of the dropouts. I had already ridden it up a short quite steep hill at the beginning of the ride and then had ridden about 3 miles maybe a little more. I was down shifting and something happened and I found myself on pavement before I knew what had happened. This is the first time I have been down in 40 years and I was more than a little embarrassed and only slightly road rashed on one knee. I picked up the bike and found the rear wheel loose from the dropout. I suppose that the QR could have been a little too loose though I haven't had that problem in 50 years of cycling but there is always a first time. Maybe I should have included this in the original post but I was still embarrassed and I did not want to confuse the original question.

I am not really sure what the screw adjusters do other than locate the axle to the RD top idler but I don't know what that relationship does in the shifting function. It must have some bearing though or there would not be the room for the axle to move forward/rearward.

I also found the wheel slightly waffled and I have since straightened that with spoke adjustment.