The quick answer is yes, it always makes sense to do usability testing where there are variations in cultural preconceptions, market maturity, language proficiency (you don't mention if it will be available in many different languages) and the like.

Whether or not you do usability testing in all countries of course also comes down to what resources you have and how you intend to make use of the findings. Many times I find it appropriate to launch and test iteratively along the way, making sure you have the budget to make continuous small improvements, making sure to have feedback mechanisms in place and placing more effort in testing and managing areas which clearly are more critical for the end-user satisfaction. But you'd never want to launch before you have something that you yourself are satsified with. My recommendation would be to do quick online tests to make sure you are not entirely off-base, and then make sure to set the iterative launch-measure-analyze-prioritize-fix process in motion.