Maybe, but that doesn't have to happen in order for a common language to exist. After all, most people on Earth are bilingual. They have a native language that they speak locally and a second language that they speak in interacting with outsiders. This has been the case for most of history. For instance, subjects of the Roman Empire spoke dozens of different languages in everyday life, but when it came to official Imperial business or trade and communication with people outside their local communities, they used Latin in the western half of the empire and Greek in the eastern half. In modern China, the main language is Mandarin (or Cantonese in the south), but most people learn English for interacting with Westerners, and even adopt Western given names for English-speakers to address them by.