If something like this happens to someone with a medical certificate and it turns out that it would be something that would disqualify you from getting that medical renewed, is it possible to let your medical expire and still go the sport pilot route? or would this kind of thing need to be reported anyhow and disqualify you from the sport pilot?
You do not need to report it to anyone.
You have to self-certify that you are fit to fly.
61.23
(2) A person using a U.S. driver's license to meet the requirements of this paragraph must—
(i) Comply with each restriction and limitation imposed by that person's U.S. driver's license and any judicial or administrative order applying to the operation of a motor vehicle;
(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medical certificate) suspended or revoked or most recent Authorization for a Special Issuance of a Medical Certificate withdrawn; and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.
§ 61.53 Prohibition on operations during medical deficiency.
(a) Operations that require a medical certificate. Except as provided for in paragraph (b) of this section, no person who holds a medical certificate issued under part 67 of this chapter may act as pilot in command, or in any other capacity as a required pilot flight crewmember, while that person:
(1) Knows or has reason to know of any medical condition that would make the person unable to meet the requirements for the medical certificate necessary for the pilot operation; or
(2) Is taking medication or receiving other treatment for a medical condition that results in the person being unable to meet the requirements for the medical certificate necessary for the pilot operation.
(b) Operations that do not require a medical certificate. For operations provided for in § 61.23(b) of this part, a person shall not act as pilot in command, or in any other capacity as a required pilot flight crewmember, while that person knows or has reason to know of any medical condition that would make the person unable to operate the aircraft in a safe manner.
(c) Operations requiring a medical certificate or a U.S. driver's license. For operations provided for in § 61.23(c), a person must meet the provisions of—
(1) Paragraph (a) of this section if that person holds a medical certificate issued under part 67 of this chapter and does not hold a U.S. driver's license.
(2) Paragraph (b) of this section if that person holds a U.S. driver's license.
If you are in doubt of or medical history would raise the question of your fitness to fly as SP in LSA, you can get your family doctor to certify if you are safe to fly with SP privileges, you don't need an AME and OK City to get involved so long as you meet all the other requirements.