No, the black box won’t affect your car’s performance or any electrical components.*
Your battery performance is more likely to be affected by the age of your battery, other faulty accessories in the car, loose battery cables, extreme temperatures or taking a lot of short trips.
The box installation engineer will tell you if there is a possible issue with your battery life when they are fitting the box to the battery in your car.
*The power usage of the box is similar to that of a blinking led, such as the one which indicates your alarm is active.