Simply put you can't have a neutral base. The way HTC coded things is that every base has to be assigned to a country.
Now if you were up for it (or somebody else was) you could create a custom base object that had no AA guns at all. The base would not be neutral but it would be unarmed. So it would sort of be like what you were describing however people could still up planes and vehicles from that base if they were part of that country.
To prevent that would you would have to create a custom base with no AA, no FH, no BM, and no VH. Then it would simply be a base assigned to a country that was capturable.
