Yes, it does now; but the Groovy runtime still has the general problem of not working with each new JVM version for months after it comes out. Whereas, with the Kotlin runtime, you can just forget about this problem and upgrade as soon as you like.
No, because Gradle isn't checking the JVM version, the Groovy runtime is. (Specifically, the Groovy compiler seems to run fine on the buildscript, producing a buildscript bytecode file; but then, upon load, the Groovy runtime seems to check that buildscript bytecode file's JVM bytecode version metadata before doing whatever-it-does when loading it.)
Gradle itself isn't written in Groovy; it's 5% Java, 95% Kotlin. The Groovy runtime is only spun up to compile and run Groovy buildscripts (i.e. the default kind of Gradle buildscript with a ".gradle" file extension.) If none of your buildscripts are written in Groovy, then you're not compiling or running any Groovy code, so that runtime check never executes.
> Gradle itself isn't written in Groovy; it's 5% Java, 95% Kotlin
This doesn't appear to be true just by looking at the Gradle GitHub repository. It claims that the code in the repo is 46% Groovy, 44% Java and 6% Kotlin
https://github.com/gradle/gradle/issues/16857