Do I have to use grout for my mosaics, or would filling in the gaps with thinset mortar (I am using thinset) be sufficient? What is the point of grouting if I can just use mortar to fill in the gaps?
Thinset Mortar should be sufficient as a mortar grout in your project.
Thinset (also called thinset mortar, thinset cement, dryset mortar, or drybond mortar) is an adhesive mortar made of cement, fine sand and a water retaining agent such as an alkyl derivative of cellulose. (1) It is usually used to attach tile or stone to surfaces such as cement or concrete. It is particularly popular among mosaicists for outdoor applications (2) - Thinset (Wikipedia)
Make sure you "use a wet toothbrush to scrub your grout joints clean as you are installing your floor (Thinset Mortar Selection).