There would be a few problems with my "putting my iPhone away" for a week.
First and foremost, it is my only phone. I am expected to be reachable by work, family, etc. Not all hours of the day, but if I just "disappeared" for a week, there may be consequences.
I also run five days a week and use the phone to track my runs. Certainly I could run without a phone tracker, but there is also the safety aspect of having a phone while running in moderately remote locations.
Lastly, it is my music player. This I can certainly do without, but I am not sure what I would be proving. I take public transit to and from work/school and use it to drown out the din of the crowd. If I am riding with someone I know (rare), I don't plop my headphones on. instead, I have a conversation.
IMO I think you (the OP) have good intentions, but you can achieve your goals without banishing your phone from your life (unless you are a severe addict to things like texting, facebook, etc.) If you are picking up your phone rather than interacting with family and friends, why not just make it a point to spend more time with family and friends? I see no real reason to stop using the phone for a week unless you are so massively addicted to the things I mentioned that you literally have to have all temptations removed from your presence.