I fully admit to bouts of rage and melodrama, but this generally tends to be in the form of an outburst rather than a general means of coping with life. I am mercurial, I'll say that much.
I personally don't go much for the descriptions that make us sound like weepy-wailey things in a constant state of crisis. I think most people (who don't know me) would see me as quiet, soft, polite, calm, rational, and mostly very stoic--I'm great at handling my pain. Those closer to me know about my outbursts and mercurial nature.
Anyway. My sister also types as a 4, and she's a lot less over-the-top than I can be. She withdraws. I thought she was a 9 till she wound up in the psychiatrist's office for her surging emotions. I would never have guessed this of her--she's universally calm and gentle, even to those close to her. She is not outwardly impassioned. She doesn't create drama.
So yes, I think 4s can be very stoic outwardly. Some can be dramatic, too. What's more important is what's happening between your ears--the inner drama is far more important to us than whatever parts of that seep out (if any).