Today, our Alliance won our 5th War to finish the 25 points needed for War chest. It took us 6 wars to fill the chest, with one lost war. This had us at 21/25 going into the final win.
After opening chest, I am now at 0/25, when I would have expected to be at 1/25. The pitty point did not carry over. This means your alliance would need to lose 5 wars before winning 5 wars before the pitty point is worth anything.
Either a bug, or poor design. It should carry over like the Atlantis summon chest does.