Fitness can be important depending on how long you are out in the wilderness. You need to be able to handle the weight you will be carrying. Strengthen those muscles with cardio and muscle training (i.e. shoulders, legs, heart). It is recommend to at least starting a workout routine minimum 2 months before departure. Depending on your weight and current physical condition it could be more or less. Doing so will help minimize fatigue, soreness, and bad attitudes. More information on how to get fit for the trip can be found at REI expert advice.
It is possible that by not being in shape you could create an emergency situation depending on the elevation. There is no concrete cause for high altitude sickness. What is recommended is for a person to not over exert themselves, make sure they have plenty of food, and they are staying hydrated. Making sure these three areas are taken care of reduces the chances of encountering high altitude sickness.