No, it categorically doesn't. Not just that, it's CPU support is quite lacking (fp32 only). Currently, there are two ways to support the ANE: CoreML and MPSGraph.
It is less about conversion and more about extending ANE support for transformer-style models or giving developers more control.
The issue is in targeting specific hardware blocks. When you convert with coremltools, Core ML takes over and doesn't provide fine-grained control - run on GPU, CPU or ANE. Also, ANE isn't really designed with transformers in mind, so most LLM inference defaults to GPU.