Can a MEMS accelerometer sensor be used as a shock sensor?
Sure you can. A "shock" is merely a large amount of acceleration over a short period of time.

You would probably want to set the MPU6050 to its least sensitive setting (±16g), and you might even be able to make use of the "tap" function whereby the MPU6050 itself looks for a sudden short sharp shock to trigger an interrupt (though that may be a little too sensitive for your needs, I don't know).