The effect of acceleration is not trivial.
Depending on what you mean by 'accuracy', acceleration has a huge effect if you are running high feedrates.
If by 'accuracy' you mean 'repeatability', which is actually what was discussed here, then it has little or no effect unless as has been mentioned, you push steppers too far and they start to miss steps. Missed steps are audible only if there are many in a row. One or two missed steps here and there cannot be detected by sound, but can add up to a big problem.
If by 'accuracy' you mean the machines ability to hold a tolerance, then again, acceleration cannot reduce backlash and cannot make the machine more rigid.
However, if you define 'accuracy' as how close the machine can follow a profile, then acceleration is king. High speed without corresponding high accelerations leave rounded corners and other anomalies. The effect is exactly like a race car needing to open up their line in order to make it around a tight curve.