It will be tricky but it's definitely possible. It looks like the rich text field store the text in a series of nested divs. So in theory you would just target the div with a class of "rich-text-editor" then count up the number of characters contained within it and any other nested divs within it. 

You can use the following as a starting point: This should print out the length of each div's contents, while might not be perfect (haven't exactly tested it thoroughly, I'll leave that to you) but it should help get you pointed in the right direction.

$(".rich-text-editor div").each(function(ev) { 
  console.log($(this).text().length) 
});

Once you have found a way to sum of the total number of characters you can then add a function that will run on click of the submit button and check if that sum is less than 4000 characters. 

Hope that helps, Good luck!