As Director of Sales for a web hosting company I had a job which required doing sales calls primarily during US business hours. I have a few thoughts on this subject:
This can either limit your itinerary to the Americas or you can embrace the timezone offset and derive value from the shifted hours.
In my situation I actually benefitted from the offset initially. Our group started in Europe with an 8-hr offset from my core team. This means I was working mostly from 2pm-midnight doing most calls during that window. As a night owl I actually dug this work style as it meant I knew I never had a call before 2pm.
This freed me up to explore the city in the morning or actually make forward progress on strategic initiatives before my inbox filled up. I think it also forced the issue of recognizing how many roles I had been performing prior and precipitated a couple of hires that might have been deferred otherwise.
Having only a small overlap window with your core team forces everyone to be hyper efficient in how they communicate and eliminates possibility of “death by 1000 meetings.” The guys from 37signals wrote about this benefit of a globally-distributed workforce extensively in their book Rework.