Does a failure to respond to FAA questions on ME disqualify for sport pilot?
Yes I believe so.

While the Sport Pilot License only requires that you are medically qualified to get a driver's license there is a stipulation that if you had been denied an FAA medical previously then you cannot just use your driver's license as your medical.  If you don't respond to their questions then you will most certainly be denied the medical.  

At this point I think it is best to answer their questions and finish out the process.  If your medical condition is under control and manageable the FAA will usually eventually grant you the medical however, a lot of paperwork, time and money may be required.  

This is why you want to do your homework before the medical and be sure that you can pass it.  If you don't pass the medical then you cannot just simply fall back to the Sport Pilot License.