Of course if you're pursuing the construction aspect of the field that is a very real situation that you may find yourself in. But first a brief overview of what logistics consists of is needed. Many people just assume it has military ties because they have heard the term fleet logistics. While this is true the military isn't the only place for these careers.
Logistics is a term used in reference to the fielding and organizing of small to large scale events. The most common form of this is the community festival that you may attend each year, or the after game party that you may plan for your kids. Though these are small scale examples they do demonstrate what logistics is at a basic level. Organizing construction efforts on a skyscraper or managing troop deployments is much harder, but the same principle applies.
You can find logistics employment anywhere that there is a need to organize and manage activities. This can range from military, construction, city planning, sporting events, catering services, and anything else that needs someone to micromanage everything. People that have a natural ability for this tend to do the best in logistics careers. To put it into perspective think about the last concert you went to or watched.
Do you remember all the lighting, speakers, the stage layout, and the special effects? You didn't think that the band did that all on their own did you? All of their equipment, gear, props, and their crews have to be gotten on site and set up before they arrive. Thus people that are skilled in logistics are needed to orchestrate things and make sure all the trucks arrive when the crew needs them. Then said person keeps track of how the riggers, lighters, and stage workers are progressing on their jobs.
It is by far an easy task. However it is essential to the band and their work. After all if it weren't for these support personnel there would be no stage. No stage translates into nowhere for the band to play at.
Although different in nature military deployments follow the same layout. Troops can be deployed but they need food, water, medicine, weapons, ammo, sleeping quarters, and latrines to support them. Not to mention mechanics and a motor pool to take care of tanks, APC's, and Humvee's. If logistics employment interests you then you will always be welcome in the military.
Aside from the military there are various logistics careers for you to choose from. Construction, demolitions, music, and catering services are all respectable candidates. There are numerous others but they wouldn't all fit in this article. Just remember you are responsible for managing everything so take your job seriously and you'll do fine.