I live out in the county so deer crossings are a daily occurring event in my neck of the woods. With the many times I've had to dip and dodge the unpredictable SOB's I can def tell you this..
With traction control on working properly and stock suspension (back before i lifted)..
right at the last minute making a hard turn to the left all the weight of the vehicle gets thrown to the passenger front right tire, which some of the load is then transferred across the stabilizer bar to the driver front tire essentially causing the front end to hunker down. Then as you through the steering wheel back right to get back into your lane all the load transfers smoothly across the sway bar to the driver side and the back right tire remains on the ground. The tires never slid or broke traction so the VSC never kicked in.(55mph)
with the traction control on working properly, Lifted with sway bar removed..
during the same maneuver all the weight is immediately thrown to the front right tire, after making the hard right turn back towards your lane the load somewhat violently lunges to the drivers front tire, the back right tire loses all weight loads and breaks traction, then the driver's rear tire breaks traction. the VSC then cuts your throttle and applies brakes to the rear wheels individually allowing you to counter steer to get back straight. once traction is grained you have your throttle and brake control back.
no traction control, lifted, with sway bar removed
same effect as before however instead of the VSC cutting throttle and applying brakes...
once you cut back right to get back into your lane and the rear tires break traction you get started into a slide, back end cuts out left then you counter steer to control the slide, then the weight gets thrown back to the other side of the vehicle causing the rear to slide out in the other direction slightly then you counter steer once more an you got it lol..
just my experiences.. I always recommend to people though if you have a deer jump in ront of you its safer to hit the dear than to try and avoid it. plus the insurance company isnt going to cover you hitting a telephone poll or rolling your vehicle after swerving off-road under comprehensive... that would be a collision with driver at fault