ATmega328P of Arduino Pro Mini not responding
Does the MCU get bricked/locked?


Yes, it's possible. The chip requires a valid clock to run, even when programming, so if the clock settings are corrupt or were set wrong it will no longer be programmable through ICSP.


  How can I recover this?


Depending on what has actually happened you can either supply an external clock signal to the chip to get it working again, or you may need to reprogram the chip through the parallel programming interface, also known as HVP (High Voltage Programming).


  Is there any way to solve this problem using AVR Dragon board?


Yes, the Dragon can do parallel programming. You can read more about how to fix fuses with it here.