At small slip angles, the tire deforms linearly with the side-force demanded of it. This effect saturates when the rubber is essentially fully deformed. The tire then starts to slide over the surface of the road, which reduces the side-force somewhat. Now, this force acts perpendicular to the wheel plane, which is not quite perpendicular to the car's trajectory. This effect reduces the force available to turn the car and causes an "induced drag" that slows it down. The combination of these effects gives rise to the concept of an optimum slip angle.
In terms of forces exerted by the road and the tire on each other, ABS increases the force by keeping your tires in the "static friction" regime instead of the "kinetic friction". That is, objects tend to have higher friction before they begin to slip then they do after slipping. So when the system detects that a wheel has slipped, it reduces the brake pressure to the point where the wheel returns to the static friction case. (This is said to not work so well on deep gravel, but it's suitable for typical pavement.)
The other reason ABS is useful is because it allows the driver to control the direction of the force. That is, it helps you use your steering wheel to control the direction that the car moves. So one of the primary purposes of ABS is to help you corner.
If you slam on your brakes without ABS, while going around a corner, you will slide in the direction you're traveling. Since the maximum of rolling friction is larger than sliding friction slamming on your brakes will take you longer to stop. In addition, you will have no control on your direction and you will likely run off the road.
When you're stopping, your front tires take more of the weight of the car than the rear so I would think that you would lose traction on your rear wheels first. This would definitely make it more difficult to steer and more difficult to stay on the road.
But if, for one reason or another, only your inside front tire lost traction (without ABS), this would decrease the force on the tire and that would likely make it more difficult for you to turn. That is, you'd have more difficulty getting the car turned without ABS than with.
Interesting question. I look forward to see what others have to say about this.
Best Answer
No. Tread is there to account for the presence of "other material" between the tire and the road surface. For example, if there is water on the road, a perfectly smooth tire would be susceptible to aquaplaning: the water has nowhere to go, and becomes a thin film between the tire and the road.
If anything, deep profile tends to reduce the area of the tire in contact with the road, and increases the pressure. Both of these things give the "other stuff" (water, snow, loose gravel etc) a chance to get away from between the tire and the road, allowing the tire itself to grip the road.
In situations where there is a thin layer of snow (and to a lesser extent, mud or clay), a deep tire grip can shape the snow into a waffle like pattern that interlocks with the tires, and results in (much) greater lateral force - no "simple friction", but the kind of resistance to relative motion that comes about from having interlocking structures (like the teeth of gears). The deeper and wider the profile, the better the chance of a solid ridge of snow/mud being built up.
\Once you have the "intended" interface between tire and road (without the other material), the force of friction is largely independent of area, since the total normal force will be constant. But most of the time, tires slip because you are not dealing with just the road; and the profile is intended to deal with "the other stuff".