Yes. (I can never remember the official difference between contacts and vias, so I use them interchangeably.) However, an important thing on a chip is that you

Yes. (I can never remember the official difference between contacts and vias, so I use them interchangeably.) However, an important thing on a chip is that you don't need to connect the source and/or drain to the metal layer; you can connect it to something else through the silicon. You can extend the source or drain (i.e. diffused silicon) until it runs into another transistor's source or drain. There's not really any difference between silicon doped for a source/drain and silicon doped for wiring. This is especially useful when you have a single layer of metal wiring, since you can cross signals by using metal wiring for one and silicon wiring for the other.