It sounds like being able to run a bunch of Varnish servers to cache stuff at edge locations around the world. I wonder if it really works that way or do you have to change your web app a lot to work with it?
If that's what you're after you might want to check out Fastly. We're a CDN entirely based on Varnish, with all the features that implies.
I implemented exactly this for our application about a year ago. We managed to speed up the average backend response times for the entire site by about 500ms. Unfortunately, the cost of the edge servers + the anycast routing tech from a third party vendor was more than the business benefit we saw.