Even the overflow flag is not sufficient to indicate ordering in a comparison of signed numbers. Prove to yourself the following (using subtraction of 4-bit representations):
x = 1,y = -8,O = 1,x > y
x = -1,y = 7,O = 1,x < y
In this case, although the overflow flag is set in both cases, the orderings are actually opposite to each other. This means that the overflow flag, at least by itself, is not sufficient to indicate the ordering of two signed numbers after a comparison.