They do it frequently, much to parent's dismay. There is a difference between gagging and choking. Choking is when they actually get food caught in their windpipe and they can't breath. Gagging is what commonly happens as a baby learns to eat solids. Food gets caught as they try to swallow and it triggers their gag reflect, which can cause them to spit up.
Some babies have a more sensitive gag reflex then others.
What you can do to help minimize the gagging is to be selective in what you offer for finger food. Especially because your son doesn't have any teeth, you will want to choose foods that are easily gummed or dissolved in his mouth. He should be able to gum some ripe avocado, ripe banana, soft cooked pieces of apple, Cheerios, tofu cubes, cooked egg yolk, etc. Do a taste test yourself to be sure. You should not rely on this information as a substitute for personal medical attention, diagnosis or hands-on treatment.