I think there can be a distinction between the two terms. A person can choose to read widely, collect nice things, and enjoy the finer things in life without totally giving up the need to live with all the necessities of life. For example, a cultured person can choose to live away from civilization in the barest way possible without it affecting his knowledge and love of things that are important.
To "be civilized" is usually an idiomatic expression that refers to a person's deportment, or behavior, toward other people: it is synonymous with to be or to behave with civility.
Civility entails respectful courtesy and politeness in addressing, or speaking to, other people and in one's general treatment of other people. To illustrate, bullies can never be civil, or "civilized": bullying completely contradicts the definition of being civilized and civil.
Cultured people have finely developed taste for and knowledge in the finer things in life from fine art to ballet to fine wines and things in between. It is entirely possible for a cultured person to have an uncivilized, uncivil, deportment and to speak to others and behave toward others without respect, courtesy, politeness, or kindness.
Therefore it is entirely possible for cultured persons not to be civil, or civilized, in their deportment, or behavior, toward others.
One definition of "culture" is "the quality in a person or society that arises from a concernfor what is regarded as excellent in arts, letters, manners, scholarly pursuits, etc." One definition of "civilization" is "an advanced state of human society, in which a high level of culture, science, industry, and government has been reached." (Both definitions from dictionary.com)
So, one is cultured if one has an appreciation for the arts; one is civilized when one has attained a high level of appreciation for a wide variety of human endeavors, including but not limited to the areas covered by being cultured. Yes, it is possible to be cultured without being civilized.
A character that comes directly to my head when I read the previous postings is Hannibal Lecter in The Red Dragon. This book takes us straight into the mind and life story of Dr. Lecter. We learn how his genius was evident in everything from the wealth of knowledge in his field of study, to the elegance with which he treated nature, being able to capture the smells of herbs, making succulent dishes, and knowing by name and year the best wines. Yet, he is a sadist whose traumas from childhood impede him to lead a normal life. He tortures, kills, and dissects his victims. He is a social monster. That makes him automatically uncivilized. Therefore, the answer to your question is yes.
The world civilized contains a value judgement. We usually refer to it as having some kind of relatively advanced structure. Any behaviors of a group basically make up culture. Culture can be what we do not consider civilization.
This reminds me of Lord of the Flies. The choir boys came into the congregation of the other boys in the first chapter and they were very cultured. They had on their uniforms, they maintained an order, and they conformed to the requests of their leader. Obviously they had some norms for how they lived.
However, as the book continues, their value of human life recedes. Character after character has their blood spilled at the hands of these choir boys. A civilized person would not take human life from another.
It may be that a transformation took place because of their circumstances, but I think we can clearly see being cultured does not mean also being civilized.
If you are thinking about this in literature, a perfect example of such a person is General Zaroff from "The Most Dangerous Game." He is a person who is extremely cultured, loving opera, good wines, and other such things. However, he is, at the same time, willing and eager to hunt and kill other human beings. This is surely a person who is cultured but not civilized.
I completely agree with the previous posting. for me, I think about it this way: there are many people in society today that people consider book smart, but not street smart. In the same way, people can be cultured, but not civilized. These people understand the aspects of a culture, but based upon their inability to relate to others forces them to lack substantially in the civilized department.
This entirely depends on your definition of these two terms. I immediately think of the way that so many of the Nazi High Command were definitely cultured in the way that they enjoyed and appreciated aspects of art such as opera and painting, but at the same time they showed they were not civilised by their barbaric decisions to exterminate millions of Jews.