Should I file the application without the Status Information letter from Selective Service?

Generally the failure to register with Selective Service due to not knowing the requirement will not stand in the way of naturalization eligibility if the applicant is already over age 31. The USCIS indeed may require that the applicant show that he attempted to register but was declined because he now is too old to register, and while that generally should be submitted as part of the naturalization application package, it may be possible to submit it at a later time. This is one of many issues that can be significantly more complex than it may appear just from reading the naturalization application instructions and the immigration statute itself, and it would be wise for you to work with an immigration attorney in the naturalization application process.