Allows Markdown a table without header or has this to be done with CSS?
In short, no. This is a good post about the issue:
as you said, one way is using css to style (or hide) header, of course you can always use HTML in your md file.
my tip here, you can also use html AND markdown, see:
<div markdown="1"> #Markdown </div>
That’s true if you enable markdown extra.