The European Union isn't (yet) a tearing down of borders and making everyone the same nation, although clearly neither was the Alliance given they still had their own militaries, bases and then sleeper ships. To be honest, Sirius was likely rather similar before the Nomad war, with everyone trading with each other openly and obeying agreements like the Boorman Treaty.
The Treaty of Curacao would need to be rewritten, perhaps as a separate thing entirely, if anyone else were to become a signatory. Probably the most likely participant for this first would be the Colonials, given their proximity, friendship/alliance with three of the four signatories and similar intentions to the houses. VR themselves aren't so much in this position, although I sometimes consider N.O. as a mini-CR with a bit of growing up to do to get to our level. We did have around 20 years headstart though, don't worry.
As for NATO, it isn't really anything like the RL organisation and nobody else will really join it: all it does is compare the different ranks of the BAF and LN to see who takes command of joint missions. There isn't an actual name for the Liberty-Bretonia alliance, military and otherwise.
That idea of yours Druen, sounds familiar. Suppose you are a member of the VR