Noel, There are a few reasons for using overhand knots in a strand of
pearls. Knots should be unobtrusive A pearl necklace needs knots
that are unobtrusive, and the cord needs to be free of slack between
pearls, otherwise the pearls will abrade the cord and you could lose
the entire necklace.
Overhand knots are compact, stable, and easy to position. A square
knot is not as compact, requiring relatively thicker cord for a knot
that won’t pull through the hole in the pearl. Also, I think it
would be difficult to get a square knot snugly against the pearl,
unless you had a helper holding it in position while you tied it.
Even if you did get it firmly against the pearl, a square knot is
not stable and can slip over time.
I believe that pearls are traditionally strung onto a doubled
strand of silk cord, not a single thicker cord, so the overhand knot
can take a rounder shape.