If you shoot that tightly to start with, small improvements may show up. Which ones do or don't matter depends on the individual gun. It also depends how many rounds you are putting into each group. If it is 3/8" for 10 rounds, then you almost certainly will benefit from small tweaks. If it is just 3 rounds per group, then the statistical uncertainty makes it an unknown as to whether you will see an improvement or not.
People always like to say their gun can shoot X inches or Y moa without saying for how many shots in a row it will do this. Where the error sources are random, these numbers actually vary with group size because the larger the number of rounds you put in each group, the more chances you are giving random extremes and outliers to appear. So, average group size tends to increase with the number of shots per group, even in zero wind and even if the shooter never makes a mistake. As a result, saying I've got a 3/8 inch 3-shot group gun and saying I've got a 3/4" 20 shot group gun, tends to be saying about the same thing, on average.
The above is why professional measures of precision of guns and ammunition use radial standard deviation or the smallest circle that covers 50% of the shots on the paper as the evaluator. The idea is to eliminate the more variable extremes and outliers the large test group size (often 100 rounds) permits to appear. As a result, for a given gun and lot of ammunition, those two kinds of circles tend to remain much more constant in size as you increase the sample size than overall group diameter does.
I suggest you make some ammo that is as perfect as you can to compare to what you roll now to see if you can improve group size. Rather than invest in an outside neck turning tool, invest in a measuring tool that will let you sort your cases by neck wall thickness variation. The tool will work with all chamberings and will always be useful for comparing new and old lots of brass anyway. Use the tool to sort out the best 20% and the worst 20% of your cases for uniformity of neck wall thickness. Load them identically and see if you can tell a difference between the groups they print on paper. I would shoot 15 shot groups for statistical validity purposes. You'll get some big holes in the center this way, but should be able to tell a difference more easily, if there is one. If you can't tell a difference most of the time, then case neck wall runout isn't the biggest source of error in your system anyway and you need to look somewhere else for further improvement. If you later identify that source of error and get that further improvement, then go back and retry the top and bottom 20% neck wall runout brass to see if it then shows a difference.