Your query has so many shades! You'd better be able to define contentment.

Is contentment defined in that you are happy with yourself? I guess you might. Better a question to raise with a therapist or two or three!
Case histories indicate closet crossdressers might fit your query better, because I can't see how one can be MTF and be contentedly closeted. I can conceive that it could be done. Yet what strength of personality is needed for that though! For some of us its not what we wear in public but how we act and interact with others that reflects gender. Of course we prefer to be pretty and well liked. But we can't all be Elizabeth Montgomery, or Princess Diana.
If its all tangled up in the safety or lack of it when out on the street or at work, with fear of rejection and ostracizing behaviors of others, then I guess you could say staying closeted is safer, but I sure wouldn't call it contentedly closeted.
I don't know that its all about what we present to the world. Are you talking about dressing up or down in private? Or, living as something other than yourself? Or, presenting what you don't feel in public? If truly MTF then it should have shown up in one trait or another, and you can live it. We can all be trained to hide our true selves, but I think you'd be hard pressed to describe it as contentment. I think we all are closeted about one thing or another, we just call it self control.
I just don't like the term "closeted." MTF is a description of how you present to others, either in your personal or public lives. Gender identity is what you feel and live and act. "You" will show through no matter what, no matter the trappings. Hiding a personality trait can be done with skill, albeit maybe in shades of personality.
I'm not saying this very well. I think its no different than wearing a blue coat one day and a red one another. We are all able to shift our behaviors and presentation to match what we think we need to do to survive.
When personality is hidden, hidden, hidden, it damages the psyche. Those of us who stepped out have the satisfaction of fulfillment that precludes ever going back. Letting our true personalities through is something done unconsciously. I don't even know how one could even be closeted and be MTF. Hiding causes more internal strife and stress.