"Мне бы быть/стать вечно пьяным" is implied. Structure of phrase is incorrect, omitting of this word is wrong. It imitates another pattern "мне бы verb|в/на place". For me it's strange because it's not hard be express this idea in correct form: "Стать бы вечно пьяным". However "художника каждый обидеть может" (tm).
So it expresses wish to be eternally drunk.