>>58460275No, it is not a restricted or special legendary. Furthermore, it does not actually form a trio with Ho-Oh and Lugia.
The Pokémon that goes well with the birds of Johto, I would say, is Regigigas, because they are all masters of trios, large Pokémon with high stats, one referring to the sky, another to the sea, and the last to the earth. The duo seeks a trainer with a pure heart, while the other protects ancient human civilisations before being sealed away.
But alas, there is no official link between these three.