I did some more reading on this, so I might be able to provide an answer.
It seems to serve 2 purposes.
1) Allow release of gases during manufacturing such as MistaEng suggests
2) Relieve stress during compression, such as when pressing a HSF onto it.
Since it is open to the core, It might also serve to relieve the expansion of air under the heat spreader. But the material
is not solid, and should still allow for the pressurized air to seep out.
What I don't know is if the heat sink and heat spreader connection is air tight. If it is, then filling the hole is no problem.
If it isn't airtight, then the hole would certainly permit the exchange of gases near the core during operation. Filling the hole might make this less efficient, resulting in increased heat. But I think that once the air pushes itself out the hole the first time, it will create a permanent escape route.
As far as using a conductive paste: If it ain't smoked yet, I wouldn't worry.
I suppose you could use a micro vacuum to pull the grease out...