I've never driven a car with that kind of suspension, does the design still use caster to self-center the steering, or will the tires stay roughly where you point them even if you let go?
Yes, you have to have caster or the car would be very difficult to drive. I had a VW bug with a worm gear steering box that was going bad. It would almost keep the wheels wherever you put them and it was scary to drive. Think about how you let the steering wheel slip as the wheels return to straight when you turn onto a cross road, you had to return the wheels to straight yourself.
Rear wheel drive cars also do it. The caster on a car mimics that of the wheel of a shopping cart. Having the pivot axis be at a slight angle relative to the direction your travelling makes the wheels trail behind that axis.
It does tend to be more apparent in front wheel drive cars, perhaps it's the weight of the motor? It's really important to get right in motorsport, as it denotes the characteristics of the car when you've oversteered. A car with correctly set caster will "self steer" itself back to straight without any driver input, and it will guide the car while oversteered in a way that's balanced with the direction the car's actually heading rather than where it's pointing (if you're intending to be sideways, like in drifting).
