It does depend on the size of the circle or arc, and on SU’s minimum distance at which it considers two points are meant to be coincident (about 1/1000 of an inch). It won’t draw circle/arc segments it considers ‘too small’, which is probably a good deal longer than 1/1000 of an inch.
But in a circle with 1000ft radius, I can set the number of segments to 999 (the maximum that the Entity Info dialogue will accept).
By further experiment: at 10inch radius, the maximum is 444 segments, and the length of a segment is 0.142 inches.
You could experiment yourself to see what the relationship is between radius and maximum segments, and see if you find a pattern. It can’t be as simple as a fixed minimum segment length, otherwise you couldn’t draw small circles.