Using the spare tire supplied with the vehicle will not affect the performance of the RWAL or system.
Tire size can affect the performance of the RWAL system. Replacement tires must be the same size, load range, and construction on all four wheels.
Contrary to popular belief ABS brakes will not stop your car faster. The idea behind ABS brakes is that you maintain control of your vehicle by avoiding wheel lock up. When your wheels lock up you have no steering control and turning the steering wheel to avoid a collision will do you no good. When the wheels stop turning, it's done and over.
When driving on slippery roads you need to allow for increased braking distance since the wheels will lock up much easier and the ABS will cycle much faster. Speed is a factor also, if you're going too fast even the control ABS gives you will not be enough to overcome plain inertia. You may turn the wheel to the left or right, but inertia will keep you going forward.
If there is an ABS failure, the system will revert to normal brake operation so you will not be without brakes. Normally the ABS warning light will turn on and let you know there is a fault. When that light is on it is safe to assume the ABS has switched to normal brake operation and you should drive accordingly.
I hope that this has helped you understand how ABS systems work. It is a technology that has been in use for many years before it was adapted for automotive use. Aircraft have been using some form of ABS since WW II and it is a tried and true system that can be a great help in avoiding accidents if it is used as it was meant to be used.