It depends on what you mean by "military unit". If you make your own miltary units (by profession assignment) from free colonists, indentured servants, or petty criminals, then (yes) you can always train them at Indian camps. And you don't even have to ask them to put down their firearms to do it. Pioneers that you make yourself from free colonists, etc, likewise, can be trained at all Indian camps.
Dock military units however, can not be trained further at Indian camps because they are already considered specialists. If you clear a specialist's profession then they become a free colonist again, which you can train at an Indian camp, or school in your town's educational building.