I have done this, however longer, and it is not a problem.
I have used an unlocked Verizon iPhone and had no problems. Well, ALMOST, no problems. ;)
I bought the service (which, with Google Maps, Google Translate, Youtube, and surfing, lasted 3 weeks) and let them insert the SIM card and get it 'working'. It took a few minutes so they handed it back and said something to the effect of, "It may take a little while--stop at another store if it doesn't start working in a little while." So we sat in the store until it started working--which--after 20-30 mins--it DIDN'T. We politely gave it back to the clerk, she did some stuff on her computer and, poof, suddenly it worked.
Rule #1: DO NO LEAVE UNTIL IT WORKS. It is infinitely easier to get it working at the airport (they are EXPERTS) than to find another store somewhere else. If you follow this one rule you will have 20-30CHF service that is at least as fast and reliable as your Verizon service at home. We went through Salt/Orange.
When the data inevitably ran out it prompted me and allowed me to 're-up' while on the road several times with no issues.
EDIT: Get the ZRH Zurich Airport app for iPhone
which will tell you ALL kinds of stuff and how to access SO many services and shops. If you do end up waiting for your phone to activate go to the observation deck for 5CHF per person. Worth it!