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A couple of things, a limited slip/posi unit is very different than an open diferential. Even an open dif uses spider gears which when you place enough load on them will cause the drivers rear tire to transfer power to the ground. However, if you accelerate moderately it will not force the axle to rotate at the same speed or torque as the passenger axle. You can in fact help an open dif by adding traction bars. IN this case the IRS setup would aid in making even an open dif spin both wheels. Once the drivers rear breaks loose it will remain locked until you let off the throttle or the car accelerates enough to reduce the load and then it will release. I had a 69 Camaro, 71 Chevelle, and a LeMans that all had open difs but out of the hole always 'caught posi'. I also had several old cars and new trucks with a true posi dif. They have clutches in them which lock both wheels. GM calls them limited slip. They take special limited slip lubricant additive to keep those clutches working correctly. GM also makes a "locker" rear dif and that is antoher beast altogether. Those are typically only put in trucks due to how they lock and unlock they are more built for low speed locking that releases at about 20 to 30 mph. But now I am getting off topic.
A limited slip will lock both axle more easily and keep them locked. It takes more (power and chassis setup) to get an open dif to lock. If you jack up a car and spin the passenger wheel by hand, the drivers wheel will spin in the same direction on a limited slip and the opposite direction on an open dif.
In the snow, an open rear dif will help keep the car straight if the rear tire loses traction. It hurts if you get stuck though because it will not lock the drivers axle to get you out. Traction control reduces power transmitted to the ground of a slipping wheel. It will help in snowy conditions but will reduce the power to the ground and slow down acceleration which isn't good for racing type applications unless the driver has less ability and control to manage wheel spin and maximize traction than the computer can.
As far as GM not putting limited slip in only the V6 automatics, I can not think of any logical reason. All the axles housing are the same. The only change is the differential itself. They already have the 3.27 gear in some SS's, so it isn't a carrier issue. The cost of the unit is several hundred dollars more, so maybe they felt like they could save the coin because in their research the people who buy the v6 auto are not as likely to notice or care. Again it will act like a limited slip in some cases due to the 300 hp and the way the IRS is set up.
To test if you have limited slip or open, put the passenger rear tire on some ice and see what happens when you accelerate. If it is open, you will just spin the right rear tire because you can not get enough traction to load the spider gears to lock the axle. A limited slip will immediately grab traction with the left rear tire and accelerate right off the ice. Make sure you turn off traction control so the computer doesn't interfer with activating the brakes.
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