Should I submit the application and will it basically be auto-denied?

Generally, registration for selective service is required of Permanent Resident males age 18 - 25, and those who fail to register because they do not want to be registered can be ineligible for naturalization due to lack of good moral character and/or lack of attachment to the laws and Constitution of the U.S. Failure to register because one was unaware of a need to do so, however, is different. For a male between the ages of 26 and 31 who failed to register to nonetheless remain eligible for naturalization, he must demonstrate that his failure to register was not a "knowing and willful" failure. For this, the person may seek a status information letter from the Selective Service showing a current attempt to register, showing they were not permitted to register because he is over age 26, and confirming that they failed to comply with timely registration. At a naturalization interview/examination the USCIS adjudicating officer will question the applicant under oath on this subject in order to make a determination about whether the failure to timely register was knowing and willful. The officer may examine a sworn declaration explaining a failure to timely register and may examine other evidence of an applicant's good moral character. For a male who has reached age 31 (five years beyond the maximum age for registration requirement), the immigration legal analysis is different. It would be wise for you to work with an immigration attorney in connection with your goals of becoming a naturalized U.S. citizen.

It may not be auto-denied if you can show certain things. Consult with an attorney.