Definition from Merriam-Webster.com is: a person given to often excessively emotional performances or reactions (first date 1979)
I know no one back then would call anyone a "drama queen". And per the above definition, Fanny Dashwood fit this quite well on the occasion for her reaction to Lucy and Edward's engagement. You're probably right - Marianne wasn't overly excessive. She just let it all hang out emotionally and didn't try to reign it in. From a conservative viewpoint (or say, in comparison to Elinor), Marianne was excessive. But from a more neutral standpoint, she was merely natural.