This is an interesting construct and a great question.
Let's start by explaining it this way: Instead of using the proper name, use a generic word instead. Then the sentences will make a lot more sense:
Yesterday I met an angry woman at the cafe.
The astounded man could not say a word.
Those probably make sense, and articles do not seem odd or out-of-place.
When you substitute the person's name for the generic word, the sentence carries more meaning.
Yesterday I met an angry Kate at the cafe.
If I heard this, I would assume:
- You and I both know Kate – this wasn't some random stranger who was angry
- Kate is not usually angry – this isn't her usual mental state
Therefore, I'd probably answer with something like:
Oh? What was she angry about?
What happened to Kate?
The astounded John could not say a word.
That pretty much says the same thing as
John was astounded and couldn't say a word
but it has a more poetic ring to it; you are ascribing a state of astonishment to John.
As for the other example in your comment:
Mike was accompanied by the beautiful Sara Hope.
This is different; in this case, I would interpret the definite article to mean that Sara Hope is a person with some fame or celebrity, and Mike was with the famous celebrity, not some unknown person who happened to have the same name.
At any rate, these constructs are grammatical and valid, but they are also a bit unusual. I would caution against overusing them in casual conversations.