Correct, Gradle doesn’t use the GRADLE_HOME environment variable. There is a similar concept of gradleHomeDir in the API, but this is the location of the distribution running the build. This would be the same path as GRADLE_HOME if you’ve installed Gradle as listed in Chapter 3 of the User Guide, but there’s really no relationship unless you’ve created it yourself in setting PATH.
Just as many Java tools use JAVA_HOME to help locate a JDK/JRE, there might be a tool out there that depends on GRADLE_HOME being set to help find your Gradle install, but this should be a rarity given the predominance of the wrapper and that PATH is usually searched as well. This is besides the point though because it would be affecting that tool, not the function of Gradle itself.
There are a few environment variables that Gradle does read (including GRADLE_USER_HOME), which are detailed in the Build Environment section of the User Guide.