The short answer is yes. The long answer is yes, very much so.
One of the hottest topics these last few days is the tragedy that befell the yellow Proton X50 resulting in its total loss. This particular car happened to attract a lot of attention because of the way in which the owner modified the car almost immediately after purchasing it - not merely in terms of aesthetics, but various other mechanical components as well.
It even had its power uprated, which wouldn't really be an issue considering how both the tyres and brakes were also improved almost immediately after purchase. It does beg the question though: Can car modifications affect the various safety systems in your car? The simple answer is yes - and here's why.
How These Systems Sense And Work
The way in which these systems actively read the conditions and what the car is doing are through a variety of sensors. Active safety systems may use radar or LIDAR, or even stereoscopic cameras to "see" the road ahead. The more common traction and stability control systems, as well as anti-lock braking systems, rely on wheel speed sensors to tell the computer what's actually going on.
Obstructing any of these sensors can obviously cause issues, which is why many active safety systems will have trouble in heavy rain or other dense conditions. More traditional safety systems don't always suffer from confusion unless the tyre and wheel size is changed in some circumstances - especially when your car came with a specific ratio of front to rear tyre size.
No matter which system you're referring to, it all comes down to how the brakes are applied in order to bring the car back under control. Think about it: in the event of collision mitigation, the brakes are hammered as hard as possible. When your car is oversteering or understeering, the system applies brakes to different wheels in different amounts to stabilize the car. Traction control - well, that's clever throttle manipulation, so it's an entirely separate issue.
How They Decide What To Do
All of these sensors and components are naturally very expensive - more complex systems with faster reaction times, such as the 4-channel ABS module from a Porsche may run well into the five figure range. But they are all absolutely useless or far from effective if they aren't calibrated, which is the job of engineers at a manufacturer.
Hundreds upon thousands of hours are put into the development of a car, and then the safety systems are calibrated for the car on top of that. In the same way that a human can naturally correct oversteer (when your car starts to buang), the major contribution to an accident is still whether correction is applied precisely and in the right amounts.
Engineers will calibrate these systems for a car based on the parameters that the car is sold with - the standard suspension, the standard stopping power of the brakes, and of course the relative amount of grip of the standard tyre option in various conditions. Each of these components can greatly influence how much correction the safety systems have to apply.
How Modifications Can Cause Problems
As you can imagine, the calibration for these safety systems can be pretty tight. For example, upgrading your front brakes to larger components may result in the system applying too much stopping power on the front wheel, causing it to behave even more unpredictably when you're in a tricky situation.
On top of that, stiffer suspension (contrary to popular belief) actually makes a car more likely to lose grip. You may feel as though the car is more stable, but what stiffer suspension also does is narrow the threshold between grip and loss of grip, and that is why swapping to a more aggressive suspension setup can cause safety systems to react perhaps a little too slowly, or with not quite enough input.
And of course, there are the tyres. Going to a very aggressive tyre designed to work in the dry is usually the choice for those seeking performance, but you give up more than what you gain when it comes to driving in the wet. This also means that your safety systems such as ABS and stability control may not function as well, simply because they have less grip to work with.
At the end of the day, whether you choose to modify a car or not is entirely up to you. Some of us go as mild as getting better tyres, while others go as far as swapping entire engines to change the way a car feels and behaves. As long as you understand and accept that you may be compromising some of the safety features engineered into a car - and probably get some proper driver training - then you should be okay with what may come your way.