I'm not sure about the size of the puffer fish in question, but a confrontation could go either way.
If you are actually of a mind to keep the puffer alive, and the mantis, they should NOT be housed together.
Even if the mantis didn't kill the puffer, he could maim it with a strike or 5...
I watched one of my mantis smash tentacles off of an anemone that I added two days ago...I have since moved the anemone to another tank, but that poor thing...Watching Mantis smash apart rocks should/would keep you from adding a fish that you cared about (not to mention the $$$ involved).
Hope that my comments may have helped.
-Ron