Yes, how long it lasts depends on how it was treated.
I assume the wood I have taken down was treated by painting it on. The other method is to pressure treat wood.
With pressure treated wood the wood is put into a chamber, which is flooded with the treatment solution. Then the pressure in the chamber is increased quite high, this forces the air out of the wood and the treatment goes much much deeper.
Pressure treated wood lasts many many years outside and is not affected as much by water. It's much more expensive, but for roofing I think it is worth it.
RE: Taking down our terrace roof - part II