Highly doubt it. REST does the job quite sufficiently. Plus APIs service more than just web browsers. A comprehensive set of client adapters will be needed before an effort like this would ever be considered by a large company.
Even though I found the concept intriguing, I stayed away from GraphQL because of the Facebook licensing issue. My company has stayed away from any open source technology published by Facebook. (I haven't revisited the issue for a while, but it looks like the licensing debacle may have been rectified by Facebook.)
I instead tried out Netflix's Falcor, but it just wasn't mature enough at the time to adopt.
Microsoft has also had a enhanced REST technology out in the wild for many years, called OData (I'm really fond of OData). However, it has yet to gain widespread adoption despite adding features similar to GraphQL, like (quasi-) graph traversal, filtering, and projection. It could be because lots of developers are allergic to anything Microsoft or, more likely, it could be that standards take a long time to be adopted at large.