It depends. As the universal language, English is sufficient. If an English native is in other country, perhaps learning the local language will be good.
More than the language it is understanding of other countries culture and realities that is matter, especially local knowledge.
Say for example, Mandarin - At best it is a local language and not Asia wide. In India itself there are 26 languages with 10 major languages. Spanish will not cut in Asian countries. In Gulf, once can manage with broken English and Hindi/Urdu. In Singapore and Malaysia one can survive without bothering about local language.