If that 2 oz is at the extreme ends, it may matter.
Perhaps I should clarify my statement by emphasizing that I specifically referred to "a couple ounces of imbalance" as the reason for their poor shooting. I absolutely feel that things like gun fit, choking, actual pattern density, and the very real fact that some people just aren't very good shots have much more to do with scores or hunting success than the addition or subtraction of a couple ounces at either end of the gun.
That being said, I am continually amazed that quite a few shooters insist on turning their buttstocks into Swiss cheese, or other balancing extremes that probably won't change their hit ratios in the least. There are some guns that may benefit from radical changes in balance such as stock hollowing, barrel striking, etc. Many of those guns have already been altered from their original factory configuration, such as when someone attempts to turn a heavy duck gun into an upland gun by lopping several inches off the barrels. But the vast majority of us aren't into things like high stakes Olympic shooting where one missed target in a hundred or more shots justifies radical alterations to our guns.
When I read this stuff, I am often reminded of the story of "The Princess and the Pea". Stuffing a few shells into a tubular magazine of a semi-auto skeet gun, or shooting and ejecting same likely has more effect on balance and swing efforts. The time and effort spent on magic solutions and stock butchering would be better spent on practice or shooting lessons.
. Seriously do you check your balance with the shells or out? While close to the pivot povint it does make a difference.