Can this be done by placing a socket to a breadboard, and put the chip into the socket, and just connect power then it will work?
More or less; if you want it to continue to work @ 16 MHz, you'll need a few extra parts (crystal & caps, or a resonator). Without the crystal/resonator, you would have to reburn the bootloader and set the fuses to use the internal oscillator (@ 8 MHz, IIRC). Alternatively, you could run it 20 MHz with a different crystal (and different fuse settings).
Note that for anything other than 16 MHz, certain functionality in the Arduino libraries (mostly having to do with the timers) has to be changed to continue to be accurate.