If you're willing to work with the JVM (i.e. through JNI), there's really nothing stopping you.
You can 100% make entire apps using nothing but C, C++, or whatever, as long as you're willing to interface with the JVM that's created for you to access Android APIs.
But the Android API is a JVM API. There's no getting around that. At this point, it's another OS (i.e. not Android) if it doesn't have Java in it.