Yes. Very much so. If you're looking specifically for old timey speech, there are novels written in vernacular dating back hundreds of years, such as The Romance of Three Kingdoms that is difficult for people today to read without dictionary help. Older generations of Chinese folks might be unintelligible to younger folks if they were 3 or more generations apart. There are words and slang younger Chinese speakers use that older folks tend not to say. But if we want to take a more in depth look:

First of all, we must separate spoken language from written language and writing scripts. These three things, while often related can and did evolve separately in East Asia and around the world. I won't be discussing the evolution of the script here as that is very complicated.

We could begin this discussion at any point in time and anywhere in East Asia, but I know the most about Sinitic languages. For China at least Middle Chinese, a language spoken in Medieval China through the Tang, is used as the prototypical example of Sinitic linguistic change. The reason to begin here is because Middle Chinese is a language for which we have linguistic primary sources, such as the Qieyun, that let us somewhat reconstruct the language. Around the Yuan, several families of Sinitic languages branched off from Middle Chinese, the main ones being Mandarin, Yue, and Wu. Furthermore these languages also experienced their own evolution and have different dialects/variants to this day.

Additionally, the written language in China has its own separate evolutionary history. Classical Chinese is a term for the written language used throughout the imperial era, and it is NOT the same as the writing script, and it is NOT the same as the spoken language. Classical Chinese is a sort of preserved form of an older language in China known as Old Chinese from which Middle Chinese descended from. But notably the grammar of Classical Chinese is mostly based upon Old Chinese and not Middle Chinese. You can imagine the situation sort of like Monks in Europe writing and ceremonially using Latin despite speaking a different vernacular in the day to day.

Let me note that the narrative above is too neat. Languages in history has always been far messier than the story I tell above, because of dialects and particularities specific to the time and place. For example, in Medieval China, while Middle Chinese might have been in widespread use throughout empires, dialects and other local languages might have also been in use, with the ancestor of the Min branch of Sinitic language still present in the south locally. There is no clean distinction between Dialect and language, and politics played a role, so the real life past use of language was very messy. Take what I say about historical linguistics as a simplification.

Okay let's make this more concrete. Say you're an official recruited into the empire around the 700s. You speak to your fellow bureaucrats using Middle Chinese. You write down your day's work using Classical Chinese. You go home to your family and you speak your local dialect/variant/language. Now say you're an official recruited into office in the 1400s. You will be speaking some form of court dialect based upon Mandarin, still writing in Classical Chinese, go home and speak to your family in a local Sinitic language possibly not descended from Mandarin like one from Yue. Then you might open a novel and read it in vernacular Mandarin.