Absolutely.
Changing offset affects ackerman. So in effect, if you go with a wider front offset, you are actually reducing corner entry response. The car will not want to turn in as rapidly as before, bc the front wheels are fighting each other. Think of it this way: If both front wheels are steered, like so: / /
Then the outer wheel is travelling a longer distance than the inner wheel due to the distance between both wheels (ie: the inner wheel is turning a smaller circle). However, both wheels are angled the same amount!!!
Ackerman is where the inner wheel turns sharper than the outer wheel, so that they account for the differences in distances traveled while cornering. Alternatively, toe out does a similar thing. This is why a car with more front toe out yields better turn-in response.
You can also play with offsets to affect weight transfer during cornering. Whichever end is wider is going to be transfering more of the suspension loading to the end which is narrower. Think of a car setup like this from top view:
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The above represents 4 wheels. The top is the front, the bottom is the rear. Imagine the car cornering. Now the suspension is in a “load” situation, where one side is loaded due to body roll. The wider end actually transfers some of the roll to the narrow end, as it’s easier to tilt something on a narrow platform than it is to tilt something on a wide platform. So in the above scenario, the rear of the car will want to roll more than the fronts would.
So as you can see, even playing with offsets alone can affect handling to some degree (although mostly negligeable, unless we’re talking putting fat spacers in).
Here’s the crazy complication in the scenario above (wide front, narrow rear): Putting wheels further outboard will make your motion ratio slightly lower (geometrically softer). However, putting wheels further outboard also changes how much weight is transferred per corner during cornering–in this case, the front end rolls less, despite having a softer wheel rate than it originally had. This is offsets at play.
It’s a given and take situation in all cases. Often times, we’re talking about small changes, so the net result wont be huge. But there are many factors all the time.