Not usually, do you have a recipe in mind?
I want to make a white chocolate carrot cake and the recipe calls for butter, however I want to make it with olive / vegetable oil
Hmm, could you alter this recipe to make it white chocolate?
Or do you mean white chocolate icing with a carrot cake?
http://www.chatelaine.com/recipe/quick-and-easy/carrot-cake-with-white-chocolate-icing/ (the butter is in the icing only).
No the white chocolate is incorporated into the cake. Damn this is a hard one, I am just going to give it a go and maybe substitute 1/3 of the butter with oil
Olive oil (unless you choose extra light tasting) has a pretty strong flavor that may or may not work with your cake. Most carrot cakes are made with a vegetable oil. If you are referring to a frosting (especially a buttercream), oil probably won't work.
If it's in the cake, chances are your plan of replacing 1/3 of the butter will probably work. The cake will be heavier, but that isn't necessarily a bad thing. Let us know how it goes.
Don't forget that butter is only about 80-85% fat (the rest is mostly water, with a little bit of milk solids), so if you replace butter with oil (which is pure fat) you should probably cut down the volume of oil accordingly.