You can do anything you want to a car. I've seen vans and school busses with most of the top in back cut off so that the result is an improvised pick-up. You could add a supercharger to an Aveo if you really wanted to.
But you do realize that if you got an Aveo, the best gas milage you can hope for is around 35 MPG, where if you got a Civic you could get 40, or 41 with a Corolla, and both the Toyota and Honda are bigger cars for around the same price as the base Aveo. Of course, those numbers are with a manual transmission, and I don't know if the Aveo comes with a manual or not.
My Echo gets 40 with an automatic, but since Toyota sold around 300 of them in the US, you won't find an 06. Ask a Toyota dealer if they could find you one, since they sold so crappily, you might be able to find one.