Yes, SLERP is commutative along one-parameter subgroups by definition. The problem arises as soon as more than two quaternions are to be averaged using the above procedure.

Again, using 3 quaternions and uniform weights with the above algorithm gives slerp(slerp(a, b, 1/2), c, 1/3) but medians in a spherical triangle don't cross at 2:1 ratio in general.