There seems to be a lot of misunderstanding about who "owns" the airspace of a given country.
The US - as do other countries - retain the exclusive right of use of their airspace at all times. ICAO and all airspace classes are not global "laws" and/or treaties that countries are bound by, they are standards that countries choose to accept.
Any attempt to launch a "flying server" in "uncontrolled" airspace will be met instantly with one of the following measures by pretty much any country:
1. If it is assessed as a threat by whatever definition the government in question decides to use, and it is either in geo-stationary orbit above a country or in high altitude, it will be forcibly removed by the air force. (This is why we don't park satellites over Russia. They can and will assert their authority over their airspace and everyone will agree with them)... U2 anyone?
2. If it is low enough to be tethered to the ground, it will most likely fall under local zoning laws and/or within restricted airspace, and will be dealt with pretty damn quick as a hazard, regardless of intent.
3. If it isn't tethered to the ground and also in the middle of nowhere, its "broadcasting" more than likely violates a number of existing laws, and it will be deemed illegal and shut down, but the air force if necessary.
In short, it's probably a lot easier to find a "friendly" government and host a normal server in that country than it is to launch balloons that will most certainly be temporary, or "accidentally" flown into, perhaps during a "training exercise". And no, unless TPB is now a nation, it is not an "act of war".