Accelerometer Impact/Shock
Yes.  Accelerometers measure acceleration, you would see a spike in acceleration from kicking a ball, even if the detector was on your knee.  (I assume you mean 3 axis acceleration).  The acceleration profile would be quite different from kicking a ball and just running.

Where I am employed we test our product under shock, and we use accelerometers to verify that the shock profile is consistent.  This shock profile is a waveform, sampled at 10kHz or more. We are able to confirm that the shock reaches a maximum of 250g and has a duration of 2ms.  This is represented in a waveform with hundreds of samples ever the acceleration profile.

In fact measuring distance traveled is not what the accelerometer measures; rather, through calculation of the acceleration profile the speed and distance of the motion can  be inferred.  

Aside: I do believe that your standard running pedometer does this.  They are able to measure speed quite accurately from just the acceleration profile of each step.  They integrate the acceleration to get speed.  They assume that speed was zero for that duration that the shoe was not accelerating, when it was on the ground.  They can also assume that the speed is zero at the end of the stride, so when the integration of acceleration results in non zero at the end they can subtract an overall correction acceleration.  Then they integrate speed to get distance interval.  They divide the stride length by the stride interval to get the runner speed.

I tinkered with this with my phone, wrote some software to integrate the accelerometer and it was pretty accurate as long as there was no rotation.  Rotation complicates the whole situation as you might decelerate on a different axis than you started with; but this is a different topic.

One interesting item I could detect is if you were holding the phone or if it was set on something.  Amazingly, you can not for the life of you hold your phone as still as it is when sitting on something fixed (this reaffirmed my theory that the pedometer could detect being still/planted, and thus correct for short term integration errors by assuming zero velocity when planted).  

In short, I think you could easily see a different profile between running and kicking.  A running stride profile would be a moderate acceleration with a sharp counter acceleration at the end followed by relative stillness.  If something were to be kicked, the sharp acceleration would not be followed by stillness, but rather some non-zero values as the foot is still under the limited motion control of your knee and hip.

Sounds like an interesting project actually :)