No doubt. Can’t imagine he’d be very popular if his audiences didn’t understand his language.
No matter how good one may think the Bard is/was, I doubt that he himself “coined” all of these words. Some, perhaps, but I suspect that most were either in use or coming into use during his lifetime.
For instance, one word- ruminate- has an origin listed as
152535, which is a bit before when Will was living— between 1565 and 1616. This is only one that I found, while some others seem to have their origin of sometime during his active, writing lifetime. This is not an exhaustive search of the etymology of each listed word, just a very quick perusal of the list.
But I truly don’t think that he “coined” all these words. He may have been a great writer of the time, but I doubt he had that great an extent of knowledge of all the foreign languages that would be required, which the roots of most of the listed words were taken from.
This does nothing to denigrate his literary works, but to attribute the *creation* of such a list of words to him would not only be amazing, but probably fanciful.