What is the informed basis for your decision to use a 200 g acceleration sensor?
If you are not capable of making a reasonable estimate of the acceleration experienced by a soccer ball when it impacts a surface, how do you plan to interpret any measurements you might make?
If you are serious about this project, you will have to spend some time with the available literature.
I always get a kick out of this assumption.
The pressure in the soccer ball will have some effect. The mass of the plywood will affect it, the heavier the plywood, the smaller the acceleration.
Would a 40g sensor be (physically) damaged if subjected to 200g acceleration?
Maybe. Check the datasheet. Most of them will survive overloads but 5x overload is a lot.
Could you just use a radar speed gun (doable with Arduino) setup to measure ball speed?
There are two concepts in the physics books: energy and momentum. You can use both, so long as you don't mix them.The kinetic energy of a moving body is 1/2mv2. The momentum of the same body is mv.So when the ball hits the target it transfers energy and momentum. You could measure the energy by measuring the swing back on the target. It swings like a pendulum. The swing converts kinetic energy into potential energy because it goes back and up until all the kinetic energy is zero: meaning it stopped moving.