Offshoring development

I manage a global development team for a corporation that wants to do all new hiring in a third-world country. There's been a string of people leaving, just attrition but with quite a few positions to backfill I'm raising questions of whether we want to drop our European, American developer percentage to 0% over the long term.

I think we can take advantage of timezones to manage maintenance and support better, and we have to comply with data restrictions that sometimes go as far as to require certain nationalities to view logs or release code to specific environments.

Beyond that I think its just good having a mixture of cultures and backgrounds for creativity and generally a more pleasant work environment.

Anyone been through this before? How did it turn out?