You still want to give your two weeks. I was hired for a teaching position on a Friday (I was on vacation) that started the following Wednesday. I immediately called my full time sup who I had a really good working relationship with and told him the situation. He told me that if I didn't give a two weeks notice that HR would automatically put me on the do not rehire list. I told him, I would be starting my career and wasn't going to give up an opportunity so that I could give UPS my two weeks, even though it was the right thing to do. I've never checked to see if I could reapply or not.