An engine has to burn fuel to make power. If you want to make more power, you need to burn more fuel, or to burn the same amount of fuel more efficiently. Either way, then end result is that there is more force pushing the piston down, which translates to more force that is transferred through the rest of the engine and drivetrain.
So the short answer is yes.
Something to keep in mind though is that this in only the case when you are asking the engine to make more power. When you are at full throttle for instance. If you are just driving around normally, chances are that your engine and drivetrain are not seeing any more stress than they used to.
Our Flatirons Tuning Project Car is a 2003 Subaru WRX with almost 90,000 miles on it now, and about 30,000 of those have been at Stage 2 or better. We are still using the original stock engine, transmission, and clutch, and have had the car out on the track a number of times in addition to its daily duties.
The long answer is still yes, but as long as you stay on top of regular maintenance, and make sure that you are using the best fluids (such as Redline oil or Eneos oil) to put in your car, you will most not see much additional wear on your car.
Maintenance is the key here.
If you are going to ask your car to make more power than it was designed to, you must keep up with scheduled maintenance, and if you go above and beyond, all the better.