Other than the obvious uneven/premature wear of the tires, is there any damage that torque steer may cause to the car's drivetrain or surrounding components?
It's doubtful. Almost all FWD cars have some amount of torque steer, unless they have equal-length CV/halfshafts - which is very difficult to package in an inexpensive car.
Even in extreme cases (flooring the accelerator from a standstill on a Cadillac Northstar V8 for instance) the vehicle is designed to deal with those forces and still be reliable.
Your hands and wrists might be another story.