Sadly, it would probably make us buy from Newegg MORE. By shipping the support costs off to some third-world nation that pays it's employees $12 a day, they would probably save enough to cut their total costs by a decent percentage. Some of those cost cuts will go into more advertising and lower prices, which means that they'll get even more business from us geeks who are just looking for the lowest price.
Honestly, I wouldn't be at all suprised it this really happens! Most of those freebie Newegg trinkets that they give away with their orders come from China already, and most of the stuff that they sell is produced overseas as well.