To the question in your title: No, I don't see how the atmega168 in Arduinos can be replaced with PIC microcontrollers. At least two reasons speak against it:
1) The pins aren't the same on both chips, so the arduino board would mismatch the microcontroller chip.
2) The GNU C compiler, which compiles C code to atmega 168 machine code, doesn't support PIC controllers as a target. For philosophically similaar products using PIC, search the web for "PIC Axe" or "Basic Stamp".
As for the queestion in the body of your message: It shouldn't be too hard to install a cheap surface microphone on your door that feeds into your Arduino, PICAxe, or whatever. Googling for "Arduino, microphone" yields promising hits that you might want to check out. The rest is tinkering.