I thought we were already making clear that McCoy was somehow concerned about his physical health, not mental health (see Hythlodeus' post). And that was dropped as soon as the second act began, hence it made no sense and had no point.
PTSD and the resulting anxiety, depression, loss of sleep, and other factors have physical health consequences as well. McCoy was concerned about Kirk's vital readings. Anxiety, sleeplessness, loss of appetite, grieving; they all can affect your heart rate, blood pressure, and other vitals.
There could have also been some more direct physical trauma from the attack as well (Kirk being directly in the line of fire when that massive window exploded in front of him, for instance). Not enough to stop him from doing his job during a crisis, but enough to have the very cautious doctor concerned for his friend.
Neither of those is dropping the issue, though. They simply deferred treatment until after the immediate crisis was over, by which time it was a moot point since Kirk had died, been brought back by the Lazarus Tribble, recuperated in the hospital in a coma, and a year had passed where he was likely grounded and would receive further mental care and physical rehabilitation.