To answer the original question, yes. Being a good fighter is not a requirement for being a "Good" martial artist.
Being a good fighter means you are a good fighter.
Period.
It doesn't make you a martial artist, a warrior, or a soldier.
There are many levels of "martial arts". Some focus on sports, some on street, some on combat, some on the 'deeper' with power to heal as well as harm.
But it is more than just beating people up.
MartialArtist:
Person who studies the Martial Arts
Warrior:
A warrior is a person habitually engaged in combat. In tribal societies, warriors often form a caste or class of their own. In feudalism, the vassals essentially form a military or warrior class, even if in actual warfare, peasants may be called to fight as well. In some societies, warfare may be so central that the entire people (or, more often, the male population) may be considered warriors, for example the Maori or Germanic tribes.
en.wikipedia.org/wiki/Warrior
Fighter:
someone who fights (or is fighting)
Martial Arts:
Martial arts, also known as fighting systems, are bodies of codified practices or traditions of training for unarmed and armed combat, usually without the use of guns and other modern weapons. People study martial arts for various reasons including fitness, self-cultivation (meditation), mental/character development, and self-defense.
en.wikipedia.org/wiki/Martial_artist
Martial:
military or warlike, as in: During the emergency, the town came under martial law.
www.business-words.com/dictionary/M.html
Artist:
Artist is a subjective term which describes a person creative in, innovative in, or adept at, their endeavors.
en.wikipedia.org/wiki/Artist