Yeah, you'll see a difference. Copper is also sturdier than alu, and will serve you better at clamping (but will be more difficult to machine, yes). The real question is; why wouldn't you use copper/ What's the actual price difference here?
It never hurts to coat everything, unless you really don't expect a leak to come behind the board (think... think again... see that little leak shooting upwards and dripping back behind the mobo?)