I have to respectfully disagree with this. Unless an alien is maintaining lawful nonimmigrant status, all males between the ages of 18 and 26 are required to register with Selective Service, including those unlawfully present in the U.S. The registration requirement is not limited to only permanent resident aliens.
You are correct and I should clarify my answer. If the visa overstay occured prior to age 26, the answer will be yes. However, since the applicant is over 31 at the time of filing the N409, in accordance with USCIS field office guidance, failure to register will not affect his eligibility for naturalization and he has no obligation to provide evidence that the failure to register was not willful or knowing.
Yes, since the failure to register occurred outside the good moral character period, failure to register, by itself, would generally not be disqualifying. However, it may still be considered by USCIS if there are other issues pertaining to the applicant's good moral character in a totality of the circumstances test.