Church policy seems to not affect international relations at all. It is an internal matter for the Church, and it is the choice of the paritioners to abide by it. The authority of the Holy See is suggestive. The only question that would affect international relations would be if their policy would be codified as law. It shouldn't.
International relations are always tricky on the secular level. Having the church push it's contraception policy on a formal, international level is highly inappropriate. The church is running the risk of being seen as fanatical and racist. Reproduction is the key to survival for many third world countries and should not be interfered with. That policy is very bad for international relations.