Does being unverified as a citizen affect my financial aid awards?

Just get the SSA thing sorted. It really isn’t a drama. The SSA fix will fix the FAFSA status issue which will fix any FA issues at the schools. Why are you waiting? Schools may also want to see a copy your passport, but that is for admissions. If you don’t have a passport, then your naturalization certificate copy should do it. Just follow the schools’ directions. Will you be able to get FA awards without fixing your status? I would suspect that no, you won’t have awards to compare. Contact the schools to ask.