No, the pins are slightly different order on the B than on the A - so if you want to make an adapter to map the wires to match, then it should work.

http://www.megaleecher.net/sites/default/files/images/raspberry-pi-rev2-gpio-pinout.jpg

http://www.jameco.com/Jameco/workshop/circuitnotes/raspberry_pi_circuit_note_fig2a.jpg