The green color of the 'verdigris' is from copper that used to be part of the shaft ... quite a slow process but over a very long time there will be significant 'transfer' of the copper into a mixture of copper acetate and copper oxide.I think it should be cleaned up, not for esthetic reasons, but to see if there is an issue with the metal. If it has started to leach out zinc, it will turn a pinkish shade. You can't tell unless you clean it up. Granted it would be more likely to happen under the water line, but it may well have been sitting in a wet bilge, perhaps with a wire in the water leaking current into it.
Best is to remove the verdigris, and spray on several coats of a clear urethane, etc. -IMO
The other statement of 'don't fix until its broken' is a damn good one. Bronze shafts often seize solid in steel or iron couplings, many time requiring the shaft to be cut free. The replacement cost can be 'high', especially if the replacement was unnecessary.