If I'm reading you right, you're judging the fall rate of your jig on a tight line (bail closed & rod held steady) and that's why you want to know if smaller/larger diameter lines will change that rate of fall ... correct ?

IMHO ... it would, but you probably wouldn't be able to tell all that much difference. As Alphahawk stated, it would likely be only microseconds in difference. You'd likely have to have jig weights in 1/100oz increments or even 1/1000oz increments to match up with the line diameters. Remember, different brands of mono are listed as 2lb test, 4lb test, etc. but not all of the same pound tests of those different brands have the same diameter. Even so, they're only different by thousandths of an inch. And not every jighead, even from the same brand or custom pourer is going to weigh exactly the same. And what you have on the jighead will make a difference, too. Salt impregnated plastics are heavier, and some plastics have bubbles in them and are more buoyant, while others have various sizes and shapes of tails which can slow the fall rate ... and those with feathers/marabou have less drag in the water.
What I'm saying is there are so many variables that you'd likely have to have a scientific lab to measure and corroborate all the different possible outcomes accurately.