I was struggling a bit, so I turned on the Hebrew text to speech on my mac. While I can adjust the speed, I noticed that it too combines the words. I am assuming (correct me if I'm wrong) that Hebrew is normally spoken like this (inserting pauses where most natural, not necessarily between words).
Yes, your sentence is correct. It is optional in colloquial and spoken language, but it is almost mandatory in formal Hebrew. Since this course tries to teach us a language that is not formal, האם is introduced to us, but is not used much - just in the few skills in the very beginning of the course.