Where’s Ron Levy when you need him? According to “Practical Aviation Law”, Fourth Edition, by J. Scott Hamilton, (pilots) should not unnecessarily notify or give statements to anyone, and required notices and reports be given no sooner and in no greater detail than required. Which of course is the OP’s question: is it required? Unfortunately, this book doesn’t address this specific situation, however it does set forth the requirement about a required flight crew member.
That’s it, there is nothing about whether the required flight crew member must remain the same throughout the flight. Indeed, one may commonly transfer PIC duty back and forth during any flight in a plane requiring only one flight crew member, in which case the required crew is whomever is at the moment legal PIC (as opposed to logging PIC, which would actually coincide in this case).
So as a couple of posters already said, as long as you are current and qualified to fly a C172, then the moment your friend becomes incapacitated you said, “My airplane,” and he agreed. If he is not conscious and able to agree, a reasonable person may assume he would have agreed if he could. Therefore you are now PIC and you are the required crew member and therefore no part of the flight was conducted without a required crew member and therefore no report is necessary.
However, if you are not current or certified or otherwise not qualified, yet you can fly and land the plane safely, I interpret this to mean that you are required to report the incident. I’m sure that in the well publicized cases where a non-pilot passenger lands the plane after the pilot keels over, a report was made.
However if you don’t require ATC assistance nor help coaching you on getting down and no kerfluffle occurs (the pilot didn’t die but just momentarily was throwing up because, fish) and nobody other than the two of you ever knew it happened, you could get away without reporting it, and if you did make the initial report, the NTSB probably would yawn and not require a written followup. This would be risky. If there were subsequent consequences such as another in flight incapacitation and the NTSB got wind of the first one, (both of?) you could get in trouble if you didn’t report the first one.
On the other hand, maybe they want the report even if you are qualified because maybe the point is they want to know about the cause of the incapacitation to judge if there is a risk of it happening again? If that’s the case they need to clarify the rule, I would go back to the advice to not report anything not strictly necessary under the letter of the law.
Disclaimer: I am not an attorney! Do not do anything based on anything I say! I probably don’t know WTH I’m talking about.