So I guess that's a yes to posting the private key just to see what happens?
Sure, why not, but if that $0.03 would turned into over a million dollars down the road, I'll be huntin' your ass in the furry-afterlife (or is that furry ass in the afterlife?). A million dollars could purchase a fleet of small aircrafts or supply clean water to a magnitude of people.
I would vote against it. What if someone finds out about it and sends some money without fully researching it and finding out that is has been closed and that the private key has been published? Just my humble opinion.
We can predict what will happen. If you publish it then it will end up in a lot of sweep scripts and if any funds ever get sent to it then they will be swept to another address by whoever gets lucky and has the fastest sweeper.