The answer, as with a lot of things reloading related is "it depends".
With a standard full length sizing die, outside neck turning would do very little to help improve/maintain concentricity, because it's the expander being dragged through the inside of the neck that has the final say.
Neck turning has a big effect on the evenness and consistency of neck tension you get when using bushing dies though. That will have an effect downrange. What effect? How much? Again, it depends. Tension and concentricity are also not the same thing.
Neck turning is essential if your brass needs thinning down to fit the chamber or to remove donuts (e.g. if you have a custom/match chamber, or you have formed brass).
Things I would try to answer before tumbling down the rabbit hole any further:
Is the lack of concentricity you're getting having a noticeable effect on paper?
Where is the concentricity being lost? During sizing or during seating?
Was the fella you bought the rifle from neck turning? What are the differences between his processes and equipment and your own?
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