This has always been my understanding, I mean it's right there in the name: ColdBoot HaxChi.But cbhc and haxchi are technically the same? Or am i wrong? CBHC is haxchi, but coldbooted.
Anyway, I've only ever come across one feature that CBHC couldn't handle, don't recall what it was (it was pretty trivial as I recall), but launching mocha allowed me to do it, I believe that was the first and only time I ever needed to use mocha. Everything else I've ever thrown at the Wii U from the modding scene, CBHC has been able to handle it.