Sorry, I should have made clear that my perception of the term "drama queen" includes the (fairly common, I think) element of extreme behaviour that involves drawing attention to oneself, doing things for attention and from a desire to evoke some kind of response. It's a form of inferiority complex - "drama queens" need to be validated by others because they are too unsure of themselves. That particular aspect, I think, is quite foreign to Marianne. She is quite unselfconscious, and far too genuinely aware of and deeply empathetic with the feelings of others when the moment finally strikes (as in Ch.37, with regard to Elinor), as well as being uncaring about what other people think of her.
The "excessiveness" is down not so much to her behaviour per se, I think, as to the romantic sensibility she has adopted.