Depends.. is the mini Intel Based or PPC based?
If the former, then yes, it should work flawlessly. More or less. In the past, OS X installs has included the pieces/parts to function on any platform, this may be different on an Intel Mac. I've not been willing to experiment.
If the later, then no, it won't work.
Oh.. and lastly, assuming that the hardware matches up. I have to assume that the MB's HD is a SATA, not sure about the Mini.
EDIT: they are both SATA, assuming the mini is an Intel Based one.