In essence to your question,
Yes.
Strings rust the minute it leaves the factory. Unless its sealed. Either way, when you take it out and play, it starts to rust. Coating or nano protected or not. So don't be too surprised if it rusts.
Strings die on me if I play more then an hour on new ones. What you can do to protect your strings is to get products such as Dr. Duck, Kyser Klassics Dr.Stringfellows, Fastfret (urgh) and what not out there. You can ask your local friendly guitar store for string cleaners/lubricants. These make your strings last longer, allowing them to sound 'fresher' for longer, thus you save money on changing strings every week, thus you feel happy to practice, thus you are on your way to become a guitar hero.