Generally, yes. There's still places liked Shanghai where there's a very strong local language culture, but Mandarin should always suffice.
I've travelled in parts of China (Xishuangbanna in particular comes to mind, in southernmost Yunnan) where they have truckloads of non-Han minorities, and Mandarin was the lingua franca, and got me around, but I frequently spoke it better than anyone around me on the street.
OTOH, if you travel out to say, Xinjiang, I'm told you might be better off speaking Russian - the people out there are not Han, and really don't want to be part of China. Speaking the language of the empire out in the colonies might not make you many friends :)