The Apps (+ Ads, Android, Social, & DevTools) side of Google is a Java-oriented company. Search, Geo, Infrastructure, and Chrome are all very much C++-oriented. (Inbox is very much an Apps project, so of course they would lean toward a Java stack.)
That's true, Google has very large codebases of C++, Java, and Javascript. But the C++ code base cross-compiled to JS via emscripten wouldn't help us much on Inbox since most of the interesting bits are very backend oriented.