I went without a phone for a week. Not by choice though. My iPhone 3GS got stolen the night before Apple started taking pre-orders for the iPhone 4.
And I had to go the whole week+ between preorders and shipping without any phone because the AT&T rep I talked to raised the possibility that putting a replacement SIM in a dumbphone in the meantime might screw up my upgrade eligibility, and the pending order.
I made it through without too much trouble, and so yeah, I know for a fact that I could go without my phone for a week. And I did realize during that week that obsessing over a piece of electronics like a phone is kinda dumb.
On the other hand, I don't see a benefit to not having my phone. When you do it, you trade in one set of aggravations (being "too connected," always checking your e-mail, people needling you about iOS vs. Android vs. Blackberry) for another set of aggravations (not being able to stay in touch with people, people not being able to find you as easily, not being able to just look something up and find the answer). So, it's a wash.