Not quite.. it seems the Go app is just a webapp run on the origin server(s) that their CDN pulls from. Chrome installs/upgrades would only fail once whatever caches expire.
They want to know Go can be trusted to do the heavy-lifting most people would use C++ or Java for. So far, nothing that Google has publicized about how they use Go has indicated that their concerns are invalid.
I'm genuinely interested in this particular objection. I've written several components of a multi-component system (itself just one major piece of what makes our CDN work), and it never once occurred to me to say that one component was more or less "critical" than another. In this system I've written 12kloc servers with intricately managed resources where cachlines matter, and I've written 1kloc servers that just repeatedly make internal RPCs and occasionally tweak the behavior of the system. I've seen the system's behavior when each of these components fail, and both sorts of failures cause major problems. Is one more critical than the other? I'm going to get paged and users are going to suffer whichever one fails.
The reason that people are objecting is because serving up files is not exciting or innovative and doesn't show any particular 'win' for a language -- I could write the same thing in Haskell, for example. The details about how it's serving up the files from your Googley FS are irrelevant to the non-Google employee. :)
I.e. I can run nginx on any machine with a decent CPU and saturate a 10Gbps link serving static objects.
If you were to say that the gigantic global network of awesomeness that is Google CDN runs on Go, the average non-Google employee starts to care because that's something that you can't just do with some off the shelf OSS software. Then we can start taking Go seriously for mission critical use.
That's the though process, anyway. If you don't agree with it, that's perfectly fine. :)