We speak on an out-breath so yes, we do need breath support for speech. It is true that breathing is an automatic reflex but an increase in muscle tension (e.g. due to stress) and/or wrong posture can stop the diaphragm from moving freely. What you refer to as normal speakers do not think about their breathing, that's correct, they also don't focus on their correct speaking actions. The entire process happens automatically. The reason we focus on breathing techniques in speech therapy (and in many relaxation techniques) is because we try to help patients descrease hypertension and find back to their normal, automatic diaphragmatic breathing.