Glad you asked, as this article reminded me of that. Outside of Northern China, where Mandarin is original dialect, the answer is no, Mandarin is not understood throughout the country on a level that English is in the US.
It's a kind of second language for many, with younger generations generally being more fluent than their elders. Like the Indonesian dialect, it's somewhat forced by recent government mandate except for the North where it's from.
The frequency of overhearing people asking each other for more clarification showed me that language barriers existed, even among university students. English by contrast is much more consistent and far less ambiguous among accents and dialects across the globe.
At first when people complimented me on my English, I didn't really understand why until I realized most Chinese are not fluent in Mandarin in the way I am fluent in English. It seemed they thought the same fluency disparity would exist among US natives with English.