What are the FAA sport-pilot self-certification standards?
Unless the pilot has had their certificate revoked or suspended by the FAA for their medical condition or has failed an application for a medical certificate1, they would probably be fine after seeing a physician. FAR 61.23(c)(2) states that sport pilots using a driver's license to satisfy medical requirements must:


  (ii) Have been found eligible for the issuance of at least a third-class airman medical certificate at the time of his or her most recent application (if the person has applied for a medical certificate);
  
  (iii) Not have had his or her most recently issued medical certificate (if the person has held a medical certificate) suspended or revoked or most recent Authorization for a Special Issuance of a Medical Certificate withdrawn; and
  
  (iv) Not know or have reason to know of any medical condition that would make that person unable to operate a light-sport aircraft in a safe manner.


If the holder has a valid US driver's license, it would (presumably) be taken upon the certificate holder to have "reason to know" by virtue of having a checkup with a physician to check that this condition does not affect their ability to fly safely, especially if the person involved was in any sort of doubt as to their medical condition.

However, if they have had a checkup with a physician that finds no particular issues, and that condition does not affect the validity of their driver's license, they should be fine.

1: By section (ii), the pilot must still have a medical test and pass for at least a Class 3 medical certificate, if the FAA has revoked or found unsatisfactory their previous medical under a Class 1 or Class 2 certificate.