How soon will it compost down in the toilet?

Quick answer… It won’t! Composting takes time and, unless you use the toilet infrequently, it’ll fill up before it can compost. The exception may be with a ‘long-drop’ toilet which has a larger container beneath the toilet hut/cabin. Most ‘compost toilets’ are actually ‘compost collecting toilets’, meaning you collect the solids and then add to an external larger container to actually do the composting…called ‘secondary compost containers’.