Yes, it's easily doable. Just follow this
- the copper Ninja has the same mounting system. You would only need a new 1156/1155/1150 backplate. I don't know if you can adapt the fixing system from Ninja 3 Rev. B, though.
In absolute terms, yes, copper is superior to alu. Still, in practice, the difference somehow wanes and is only marginally better. Ppl did comparisons between Cu and Al Ninjas and Thermalrights. I don't remember exact figures, but the gist was that given the price, availability and extra weight (desolate cantilever massacre of unborn sockets soaked in virgin blood) it's just better to go with Al versions.
OTOH, now that most people sell their old hi end 775 coolers for peanuts (where I live a perfectly good Ninja 1 goes for < 10 USD + shipping), it might be just fun to try it. A copper Ninja is also for sale on local auction service, priced at about 25 USD + ship. It is tempting, I admit
So yeah, if you can find one cheap, then go ahead.