MaHaGoN,
I grew up riding around Rochester in the 70's, and believe me, the streets are no worse now than they were then. I managed on a couple low-end boom bikes, and on a 1977 Raleigh Super Course (with the same skinny 700c tires you'd be putting on your Competition). I had no trouble at all until riding around campus in Potsdam, NY, when I dropped my front wheel into the openings of a metal drain grate. That only caused me to have to change the tube. I just made a point to not ride up curbs, and avoid the nasty potholes, and things were fine.
Possibly important piece of information though - I only weighed about 120 back then.
btw - it's spelled NevrDull, and it will definitely take care of your little bit of rust.