This issue is somewhat complicated. Basically, I see there two aspects:
- International presence and visibility by attending various commitees on a regular basis;
- Formal membership in the UN of the (future) Gay State.
The first aspect is very positive and should be
of course one of the priorities for various LGBT organizations, because without
talking to the people in political responsibility one seldomly achieves any progress on human rights.
The second aspect would implicate that the Gay State will (automatically??) join many international treaties and conventions, which might bring some advantages, but also some disadvantages with them. I am too ignorant of the matter to provide some funded analysis of the issue, but it seems that all in one joining the UN is rather advantageous for any state.
I would insist, however, that neither the recognition by the UN, nor the recognition by other states is essential for the souvereignity of the state. Either the country is souvereign, or it is not - and souvereign countries do not care of the recognition of others.