For a traveller the answer is effectively yes in the places you are most likely to go, and usefully no in a few of the places most worth going.
The numbers#
The Ministry of Education reported national Mandarin proficiency at 80.72 per cent at the end of the thirteenth five-year plan, and set a target of 85 per cent by 2025. The same announcement noted the unevenness plainly: sixteen provinces above 85 per cent, nine below 80, and the lowest under 50.
Proficiency also tracks age and schooling. Anyone who went through the school system in recent decades has Mandarin; the further you go from that — older people, remote villages, minority regions — the less reliable it becomes.
Where it is not the first language#
Guangdong and the south-east. Cantonese (粤语, Yuèyǔ) is the home language for tens of millions in Guangdong, and the dominant one in Hong Kong and Macau. Mandarin is understood by nearly everyone in Guangzhou and Shenzhen, but it is not what people speak to each other.
Fujian and Chaoshan. Southern Min varieties — Hokkien, Teochew — are mutually unintelligible with Mandarin and with each other.
Shanghai and the Yangtze delta. Shanghainese and the wider Wu group remain in everyday use, particularly among older residents.
The minority regions. Uyghur in Xinjiang, Tibetan across Tibet and parts of Sichuan, Qinghai and Yunnan, Mongolian in Inner Mongolia, and dozens of languages in Yunnan and Guizhou. These are not dialects of Chinese but separate languages, and in rural areas Mandarin can be a genuine second language spoken with difficulty.
What this changes for you#
Very little, honestly, with two caveats.
Your phrasebook Mandarin still works in every province. It may be the second language in the room, but it is the shared one, and using it is welcomed rather than resented.
Written Chinese does not vary. The characters are the same nationwide, so a screenshot of an address, a written name or a translation app's output works identically in Kashgar and Guangzhou. This is the single most useful thing to know here — an image of your hotel address in characters is more reliable than anything you can say aloud.
Where it does bite is rural travel in the far west and south-west, where an older person may genuinely not follow you. A guide solves it, and in Tibet you will have one regardless.
Tones, and how much they matter#
Mandarin's four tones change meaning, and getting one wrong produces a different word. In practice, context carries most of the load and people are used to hearing the language spoken imperfectly. Say the phrase; do not wait until you can say it correctly.
For the phrases worth learning and how the tones actually work, see Mandarin phrases for travellers; for the languages behind the map, China's ethnic minorities.