I am not confident that the description of a coma patient being a fighter is meant to reveal anything other than the current status of "Still in coma; not dead yet." By not dying, they are a fighter.
That being said, a positive attitude has been suggested to aid one's recovery:
"There is a science that is emerging that says a positive attitude isn't just a state of mind," [Carol Ryff, a psychology professor at the University of Wisconsin-Madison who has been studying whether or not high levels of psychological well-being benefit physical health] says. "It also has linkages to what's going on in the brain and in the body."
The full article draws comparisons to new-age or alternative medicine and should be taken with a grain of salt. But other sources make similar suggestions, especially regarding maintaining low stress levels.
Unfortunately, someone in a coma isn't likely to have any specific attitude, let alone one of a fighter. Here, we enter a collision of terms regarding personality, attitude, coma, unconsciousness. The general description of coma:
In medicine, a coma is a state of unconsciousness, lasting more than 6 hours in which a person cannot be awakened, fails to respond normally to painful stimuli, light or sound, lacks a normal sleep-wake cycle and does not initiate voluntary actions.
Unconsciousness is the condition of being not conscious—in a mental state that involves complete or near-complete lack of responsiveness to people and other environmental stimuli.
After the point of entering a coma, it is unlikely that one's attitude is directly affecting your health. The Wikipedia article on attitude isn't much help but did lead me to the term implicit attitude:
There is also considerable research on implicit attitudes, which are generally unacknowledged or outside of awareness, but have effects that are measurable through sophisticated methods using people's response times to stimuli.
But it isn't sourced and links only to Implicit Association Test which continues to discuss active (albeit implicit) reactions to stimuli such as pictures of various races. Someone in a coma is unable to respond to such stimuli. Strictly speaking, someone in a coma has no idea they are even in a coma. Even if they were a "fighter", they wouldn't realize there was anything to fight.
If there is any effect of personality on one's survivability rate of comas, the relevant effects would have needed to take place before entering the coma. In other words, if there is a general health benefit from possessing the personality of a "fighter", it could increase your chances to recover from a coma. Given the ambiguity of the description "fighter", I doubt there are any studies on this. (Admittedly, I did not look.)
Which again leads us to my original point. The description of someone a coma as being a fighter is an anthropomorphisation of an inactive, unconscious personality. It is accurate in the sense that it describes an event (they are still alive); it is inaccurate in the sense that personality probably has nothing to do with it.