I have raced a few times with my 87 GT w/AOD and street tires. I do a small burnout, and I think it does help a little with getting off the line quick. I beat a 97 saleen to the 60 foot mark, so I think it helps.
About doing a burn out with an AOD, not too hard to do, as long as you have the stock rear drum brakes that is.
Put the car in first, that is very crutial since in drive the car will try and shift once the rear wheels start spinning around 25-30 mph. Just press the brakes a little and then give it gas, dont give too much gas, just a little to get the rear wheels to spin. Once they start spinning, keep your brake preasure the same and hit the gas. I have been able to get the rpms up to 5 grand on a AOD burnout.
Another way to do a burnout with an AOD at the track is drive through the water box, put it in first and pound the gas, the burnout wont be that long but good enough.