I experience anemic to very poor results when using methods which call for tunnel-vision focus on any object, which is one of the ways to use this.
For example, in Inner Silence it's discussed how this tone can be used like the breath can be used, "to dominate our attention", but this isn't how I understand anapanasati at all, so the method described is already a little esoteric to me.
The descriptions in Intuitive Awareness are little more aligned with what makes sense to me in that they talk about a broad awareness of things as opposed to FOCUS, but to the extent that this mirrors satipatthana and anapanasati those are my preferred modalities, and to the extent that there is any difference I find myself without a reason to experiment.
I guess I'm wondering why satipatthana/anapanasati is felt to be insufficient or otherwise etc., but be that as it may. If this tone approach can sustain satipatthana and address the hindrances while aggrandizing the awakening factors, full steam ahead.
But, my experience with this sort of approach is that it leads to being zoned out - a topical mental analgesic, at best, in my case. It can feel like a calm mind without much thinking, but it's because thinking becomes difficult to do, not because the mind is well-trained.