Yes, the cat series of cars do have ackerman. However, this is a loaded question (and answer). It is not "if", but "when and where". -There needs to be clarification.
The term ackerman as we use it defines the difference in angles between the inside and outside tires as the car is turning. Generally the more you turn, the more the ackerman effect increases. Generally, with a rack type steering system, you get less ackerman than with a bell crank type of system.
A rack system has two ball joints set at a fixed distance appart, and maintain an equal distance between those two points throughout the steerings' range of motion. As the steering system moves left to right, there is little shortening of the entire steering linkage. This is especially true when you first start to turn the steering system left or right. This means that off center, you will have very little ackerman and the car will tend to initiate its turning more quickly (then with a bellcrank system).
A bellcrank system on the other hand has two points that are fixed (via the center link), and two points (the outer link balls) that vary the distance between them according to their position in the steering range (usually shortening off of center). This means that there there is an immediate deviation in length as soon as the steering begins to move off center. The more the steering moves tward its end point, the shorter that distance becomes. This translates to more ackerman (usually).
One other thing to consider is that the length of the steering arm itself will effect how the system works. As the steering system moves left and right, the links on a rack will move rearward, causing the steering linkage to effectivelly change length. This will also effect ackerman

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This is a simplified explanation however, as the angle of the tierods running out to the steering system knuckles also greatly effects how much, and when your ackerman really comes into play. This is especially important on the Schumacher cars because of their extreme/crazy steering link angles. On the Cat series of cars the links are angled really far forward. This means that when the steering rack starts too move left or right the tierods angle even more greatly and begin to pull in the outside wheel in creating ackerman. However, this doesn't come into play untill the end of the range of movement. So with the cat series of cars this means that there is little ackerman in the beginning of the steering range, and alot at the ends of the range. It works kind of "exponentialy" if you will.
So how do you use this info? Well, typiclally a rack system is better on loose surfaces because it gives better steering response off center, and the loss of ackerman isn't felt because of the slip angle of the tires on the loose surface. However, on a high bite surface you will often have the front tires binding (scrubbing) and loose corner speed. The opposite is true with bellcrank systems. Slower response off center, and better corner speed on high bite surfaces because there is less scrubbing (think RC10. Bellcranks+highbite surface = dialed). This makes the CAT steering systems a little difficut to use. On high bite surfaces, you would want to drive the car at its steering limits (because that is where your ackerman comes into play), but you rarely need this much throw. On low bite surfaces, it is good until you get to the ends of the steering throw and you have put too much steering input for the surface.
I have simplified this quite a bit, but covered the main points

. The only other thing that really effects the items discussed is tow in/out on the front. Allot of mitigating can be done with this on various systems (think 1/8th scale buggies with 3-4 degrees of toe out on the front rack type steering system). Ultimately, there are infinate variations in steering systems, and without tons of testing it is hard to settle on a perfect one for a particular car. The schumacher CAT and Cougar systems are at opposite ends of the spectrum with good in the middle and bad at both ends. Hope that answered your question. It might help to post pics

.-Jeff