It all depends,

I got some bikes that everything is a nice even patina, I took one old faithful and and repacked the BB and replaced the chain, same time I cleaned and polished the one piece crankset and chainwheel- wow it looks good clean, but not the not so perfect pedals show,
even if i service,and polish every part the paint is just shot.


my juniors- I am even considering stripping down the wheelset to polish the hubs and rims-the spokes are galv, and I can replace them the same time with stainless double butted.

what it really sounds like is you are bored and need a new project-
I would not touch the Norman- it looks just perfect just the way it is-I am looking forward to see it
polishing it would take something away, its like bronze bits on a nice old boat, it takes years to get that fine dark brown patina,