If the widebody is heavier than stock, you are adding weight. Just like adding a subwoofer, passenger, opting for the 'super-sized' meal, etc... they all add weight and affects performance, to the degree of that performance varies.
Will you feel a difference? Ask yourself if you feel the difference between a 1/2 and full tank of fuel, or if you notice the weight of a 50lb relative in your car. Odds are you won't feel a difference from the weight of a bodykit alone.
Wide-bodies usually mean heavy and wide 18" wheels. This will be much more noticable in terms of feel and performance especially in a naturaly-aspirated car. 18" wheels do change the steering feel of the car. You also hit on another good point: wheel spacers. Going wider does affect the scrub-radius of the car, leading to slightly heavier steering and feeling of the car. It also allows for clearance of aftermarket brake systems which can be a plus.
There are many people with wide bodies out there, many of which are making a lot more power with forced induction, wider tires, and bigger brakes. Look at your goals and budget and go from there, but at a minimum widebody kits require wheels, tires, wheel spacers, and the price of the body install and paint. It does affect the performance slightly but allows for more potential in terms of grip, width, brakes, etc... If done right. It can also make the car drive poorly if done wrong, but either way it will have some effect on the way the car drives.
Billy