Is it ok to paint our bronze propeller as a cathodic protection when our sea boat is made of steel? does this actually work?

What's the painting? The steel will preferentially corrode before the copper- its was the first application of cathodic protection of copper hulled ships. Apply a big current and you force it the other way but one bronze propeller is not going cover a whole ship.     

yes it is the steel hull we are protecting..just a thought as i saw one in a 6oft steel boats putting anti-fouling paints in their propellers aside from a few zinc anodes in their hulls.they claim it lessen corrosion effect due to dissimilar metal in water and coating the propeller avoids marine growth....just the same i think electrical contact exist and has probably an effect on propeller efficiency as these are not a common practise...but i have no experience on how to do protect the boats hull using electrical current..thank for the reply cloa..

Current or sacrificial anodes (which acts fairly similarly) as used given by the other boat. The antifouling paint is necesary if the anodes are protecting the propeller as its corrosion is reduced and copper ions from corrosion provide it protection against sea life infestation.  
  

Thanks cloa! i would try painting my propeller too.