Depending on how your g-code generating software handles arcs (some high level programs break the arc up and send linear segments to grbl = high g-code rate to grbl) and some use G2 and/or G3 (one g-code line per arc).
If the upper level code uses G2 and/or G3 then grbl will break the arc movement up into linear segments using the $12 setting.
Here is a comment from the source code for grbl handling the arcs (settings.arc_tolerance = $12).
The chordal tolerance of each segment is configured in settings.arc_tolerance, which is defined to be the maximum normal distance from segment to the circle when the end points both lie on the circle.
The $12 setting allows the user to select how close the linear segments approximate the path of the arc.
I have not done any testing to see the effects of changing $12.
If no one else answers with direct experience, try some small changes to see what the effect is and fine tune what is acceptable for you.
[Edit] - Well, this question caused me to wonder what the effect would be, so I did a little testing with my pen attachment to the spindle mount. Much as I expected, but this will give you an idea of what amount of change really affects the quality of the arc (this is using G2/G3). Pen marks a 1mm line.