File -> Import project… -> recognized Gradle, did its job. But is it really relevant to the issue at hand? 
It’s not strictly relevant, but I’m a stickler for details. It’s indeed Gradle fetching the Javadoc and source jars if you import that way. Gradle tells IDEA about them.
Implication is that we don’t necessarily need to have these things in central for this to work. Gradle just needs to supply them for the Gradle dependencies, which it currently does not.
I’ll have to check but I believe with my “./gradlew idea” based project will prompt me to download from Maven Central. If the idea plugin could add the sources (and what Luke said is true about the tooling api), then I wouldn’t need them in Maven Central.