Health Regulations and the Sports License

If you have a health condition that would normally bar you from being
cleared by an FAA doctor, but you do not mention it to the doctor, how
will he know? I know it is a Federal offense not to disclose - or I
am guessing it is, anyway. I am just wondering how the doc would ever
know if it isn't something obvious?

Second question: can I take flight classes as if shooting for a
regular pilot's license and then when I am done with the training just
apply fo the Sport's License? Does the one qualify me for the other?
What is going on is that there is a perfectly good flight school in my
area, but they do not train specifically for the Sport's Pilot
License. It would seem to me that I could go to school for a regular
pilot's license and then just qualify for the Sport's License with
that training plus a driver license and skip the medical exam. Right?
Or am I missing something?