Can olive oil be substituted for vegetable oil in making a box cake mix?
Yes. As far as the mix is concerned, oil is oil. You're not reaching high enough temperatures to worry about smoke points or anything, and you're not trying to use a weird substitution (applesauce or some such).
That said, I've done this before, so I can tell you that it may affect the flavor of the finished cake-- vegetable oil is called for because of its neutrality, but olive oil (especially the good stuff*) often has a distinct, fruity flavor. Depending on the (quality, quantity) oil that you use, that olive-oil taste may come through in your cake. Whether that's a bad thing or not is up to you.
(*I and many others would consider it a total waste to use good extra virgin olive oil in a cake. I can't speak to any health reasons you may want to substitute, but if it were me and I just didn't have any vegetable oil on hand, I'd either go to the store now or wait to bake the cake.)
Yes, but. It will affect the perceived richness and possibly also the flavor.
I have successfully substituted half the oil called for in a brownie mix with olive oil (because I ran out of canola oil). In that case, it gave the finished product a real richness. When I used all olive oil with the same mix, there was a noticeable olive oil overlay to the finished product which was unpleasantly "healthy" in the context. :-)
So, I wouldn't do this with a yellow or white cake, but would definitely consider it with a chocolate, carrot or spice cake. And even then, I would carefully consider the volume of olive oil to the rest of the ingredients: All olive oil when it only calls for 2 tablespoons? Sure. All olive oil when it calls for half a cup? Uhm... maybe not.