Can you ever cough so hard you feel like passing out?

Yea: There is an entity called cough syncope where the coughing causes elevated pressure on the right side of your heart and causes a low heart rate response which lowers your cardiac output and may lead to passing out.

Yes: Coughing is spasms can lead to hyperventilation and near syncope (passing out). I had a patient do this at home, church and even in the urgent care. Very scary, but treatment lead to good outcome.