When I renewed my US passport two years ago at the US consulate in Munich (I was working in Germany at the time), I was nervous about this. I told them I had naturalised in the UK and tried to give them an "intent" letter and such. They said, we don't need any of that, they just had me strike out a portion of the application lingo and sign it, and pay them $80.
They didn't want to see the naturalisation certificate and they actually said "we don't need to see any of that documentation."
Passport was issued right away, no waits or further questions.