Of course, it’s entirely possible the rate of change within a language is not static over millennia.
If it's not, I would love to know more about this.
There are also scads of words that had a contemporary meaning that changed "overnight", morphing into entirely new meanings, which then brokered entirely new words with different definitions. My current favorite word to use an example of this is "filibuster" - the act of obstructing legislation by talking. The word, as so many in english, came from bastardizing the dutch word for "freebooter" or pirate, through a circuitous route of the French adding an S, and the American English removing an S. If you dig a bit more, you find that the "booty" part of freebooter (which means 'loves plunder' from the original dutch) came from a french word first recorded in the 1300s, "butin", which probably came from some mid-german word meaning "haul from plundering". There's also an implication that for a while in the 1500s-1800s freebooter was also the name of a private entity that engaged in exchanging goods - a "free trader", with the negative connotations falling in and out of style.
So, if you can parse Shakespeare or Chaucer at all, it's because of the mechanism of how English, and other languages derived from the same roots "evolve". Saxon and old High German, as well as Icelandic all play a huge role in the way we speak and write today, to name a few.
It depends on the culture of course. There are old cultures with the same references like a bible, that might cover longer timeframes of understanding.
It's a lot easier to ask whether contemporary humans can understand 1000 year old language, than to ask whether humans 1000 years ago can understand contemporary language.