My answer is a definite “Almost certainly no.” Back in the last century a gun writer named Bob Wallack (who was also an accomplished gunsmith), grew tired of listening to claims that the .30/30, and the lever-action rifles that were chambered for it, could never shoot accurately no matter what, Wallack took a Marlin 336, installed a match-grade bull barrel (minus the fore-end), chambered it for .30/30, loaded some rounds with match-grade bullets, and proceeded to fire groups that would have done a .308 tactical rifle proud.
Whether a cartridge is accurate or not depends on how much attention the manufacturer pays to it. Last December, I shot a .264 Winchester Magnum that turned in atrocious groups. I don’t believe it was the rifle. The ammo was from a major manufacturer, but the cases looked like they had been punched from chewed bubble gum. This is because the .264 is a small seller, and the forming dies the company used are probably 50 years old, and they’re not about to invest in making new ones.
You will probably not see outstanding accuracy from any round that does not sell a lot and whose users do not have high expectations of it. On the other hand, people who buy 6.5/284, or .22/250, or .270, or any kind of match ammo, are going to expect a high degree of accuracy, and are going to be very, very cranky if they don’t get it.
You can often see terrific accuracy from big rounds, such as the .375 H&H, .416 Remington, and .458, even though there’s no need for it and the people who use such rifles don’t expect it. This is further proof that the shape of a cartridge is less important in the overall scheme of things than how carefully it’s assembled and the quality of its components. McMillan, builder of terrific rifles and fiberglass stocks, is introducing a line of ammo called ADG (for African Dangerous Game) that is loaded to benchrest standards in .375 H&H, .404 Jeffrey, .416 Remington, .416 Rigby, and .458 Lott, and it will be very interesting to see how well it shoots. My guess is, pretty durn good.