I wondered this exact wonder this past year, so I did an experiment!
I built a concentricity gauge and characterized a couple batches of ammo for my R700 SPS Tac (.223 bull barrel), benched and bagged. In a batch of 50 rounds I separated into 3 tranches, A: 0-3, B: 3-10, and C: 10-30; units are 0.01mm of runout, measured at the leading edge of the bullet's major diameter vs the case shoulder and case base.
I found. . . no difference whatsoever in group size! I shot the groups across 3 range trips, A, B, C, B, A then C, B, A, B, C, etc. I was a rigorous as possible within the constraint of 50 rounds (and I design test plans for a living).
I'm certain that concentricity effects accuracy, but I have proven to myself that with my equipment and my average group size of ~1 MOA, it's not measurable. After I've shrunk my groups down to ~0.75, I"ll rerun the experiment and see if I can measure the effect.
If you don't yet have a gauge, save your money and do your own experiment; take a batch of 50 identical rounds and separate them visually by rolling across a flat surface and looking for wobble. Shoot your 10 best and 10 worst, and see if you can measure a difference.
Edit: I also found that, just as Redding will tell you, the vast majority of runout is caused by brass (neck thickness and modulus variation) and the sizing die. The seating die doesn't seem to matter at all. This discovery cost me a $100 Redding seating die; it's wonderfully adjustable, precise, and repeatable, but the ammo it produces is no more concentric than what I make with my roughly-finished Lee seater.