Not necessarily - the unlock is handled by the MOBO Bios so you would need to set the settings correctly in the Bios again for it to be unlocked (and the MOBO would have to have the proper support for unlocking.) - Unlocking the 4th core does not permanently change anything on the CPU so once you change it to another MOBO it is just like installing it for the first time (though once you are succesful in unlocking it and it running stable the chances are it should be unlockable on another MOBO that supports unlocking.