that's a odd question. not sure what you mean. I don't think that shouldn't be used as criteria for discriminating polar from nonpolar. Think about all of the molecules you've encountered in your DAT study. 99% of them probably have unpaired electrons.
Two methods i use to determine non polar:
1) Is the shape of the molecule such that the poles cancel eother out. For example CCl4, ie tetrachlorocarbon. If you can imagine the molecule where all 4 Cl atoms are "hogging" electrons in their respective directions. Each bond is polar but the net polarity is 0 bc the vectors are cancelling each other out. A binary acid on the other hand (HF eg) will be polar.
2) A good shortcut is to know your molecular geometry. If a molecule is linear, trigonal planar, tetrahedral, trig bipyramidal, or octahedral in both bonding AND molecular geometry then you have non-polar. All of these cases there are 0 lone pairs on the CENTRAL atom.
for example BeCl2, BF3, CH4, PCl5, SF6 are all nonpolar. But H20 (Which has a tetrahedral bond angle geometry, but bent molecular geometry is polar)